A MeasurementBased Form of the OutofPlace Quantum Carry

A Measurement-Based Form of the Out-of-Place Quantum Carry -Lookahead Adder Agung 1 Trisetyarso * Rodney Van Meter 2† Kohei M. 1‡ Itoh 1 Department of Applied Physics and Physico-Informatics, Keio University, Yagami Campus, 3 -14 -1 Hiyoshi, Kohoku-ku, Yokohama-shi, Kanagawa-ken 223 -8522, Japan 2 Faculty of Environment and Information Studies, Keio University, Shonan Fujisawa Campus, 5322 Endo, Fujisawa-shi, Kanagawa 252 -8520, Japan Corresponding author: trisetyarso 07@a 8. keio. jp Out-of-Place MBQC QCLA Circuit The design for a 10 -bit form of out-of-place ACLA on MBQC is shown. The input qubits are on the left and output states are on the right. The propagation pattern of one qubit is highlighted in yellow. Our logical qubits are spaced with a pitch of four lattice sites. Each large box outlines one round in the P, G or C networks. The circuit is presented in unoptimized form for clarity. The out-ofplace form of the QCLA described performs the unitary where a, b and a+b are n-qubit registers. When many circuits, especially the various forms of adder, are implemented directly, communication costs limit the ultimate performance. MBQC is very resource-intensive, but can reduce those costs. By matching an appropriate algorithm with MBQC, we directly trade space for time to create a faster system. Quantum Carry-Lookahead Adder Performance • Depth is • Carry calculated by Propagate, Generate and Carry Networks The comparison of size and depth between MBQC VBE and MBQC QCLA are shown. compared to the depth is reduced to for the ripple-carry. However, this circuit costs more in physical resources, compared to Measurement-Based Quantum Computation Logic Gates • Toffoli Phase Gate • CNOT Gate • Non-Adjacent Computation References [1] R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001). [2] H. J. Briegel and R. Raussendorf, Phys. Rev. Lett. 86, 910 (2001). [3] Robert Raussendorf, Daniel E. Browne, and Hans J. Briegel, Phys. Rev. A 68, 022312 (2003) [4] D. Gottesman and I. L. Chuang, Nature (London) 402, 390 (1999). [5] P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral 1, M. Aspelmeyer & A. Zeilinger, Nature (London), 434, 176 (2005). [6] M. A. Nielsen and I. L. Chuang, Phys. Rev. Lett. 79, 321 (1997). [7] Tetsufumi Tanamoto, Yu-xi Liu, Shinobu Fujita, Xuedong Hu, and Franco Nori, Phys. Rev. Lett. 97, 230501 (2006) [8] P. W. Shor, SIAM J. Sci. Statist. Comput. 26, 1484 (1997). [9] Vlatko Vedral, Adriano Barenco, and Artur Ekert , Phys. Rev. A 54, 147 (1996) [10] T. Draper, S. Kutin, E. Rains, and K. Svore, QIC, 6, 4&5, 351 -369 (2006)