Efficient eigenvalue determination for arbitrary Pauli products based on generalized spin-spin interactions

References

• Leibfried, D.; Barrett, M.D.; Schaetz, T.; Britton, J.; Chiaverini, J.; Itano, W.M.; Jost, J.D.; Langer, C.; Wineland, D.J. Toward Heisenberg-Limited Spectroscopy with Multiparticle Entangled States. Science 2004, 304, 1476–1478.
   PubMed Web of Science ®Google Scholar
• Sørensen, A.; Mølmer, K. Spin-Spin Interaction and Spin Squeezing in an Optical Lattice. Phys. Rev. Lett. 1999, 83, 2274–2277. doi:10.1103/PhysRevLett.83.2274.
   Web of Science ®Google Scholar
• Sørensen, A.; Mølmer, K. Entanglement and Quantum Computation with Ions in Thermal Motion. Phys. Rev. A 2000, 62, 022311. doi:10.1103/PhysRevA.59.R2539.
   Web of Science ®Google Scholar
• Milburn, G.; Schneider, S.; James, D. Ion Trap Quantum Computing with Warm Ions. Fortschritte der Physik 2000, 48, 801–810. doi:10.1002/1521-3978(200009)48:9/11<801::AID-PROP801>3.0.CO;2-1.
   Web of Science ®Google Scholar
• Solano, E.; Filho, R.L.; Zagury, N. Deterministic Bell States and Measurement of the Motional State of Two Trapped Ions. Phys. Rev. A 1999, 59, R2539–R2543. doi:10.1038/35005011.
   Web of Science ®Google Scholar
• Sackett, C.A.; Kielpinski, D.; King, B.E.; Langer, C.; Meyer, V.; Myatt, C.J.; Rowe, M.; Turchette, Q.A.; Itano, W.M.; Wineland, D.J.; Monroe, C. Experimental Entanglement of Four Particles. Nature 2000, 404, 256–259. doi:10.1038/35005011.
   PubMed Web of Science ®Google Scholar
• Meyer, V.; Rowe, M.A.; Kielpinski, D.; Sackett, C.A.; Itano, W.M.; Monroe, C.; Wineland, D.J. Experimental Demonstration of Entanglement-enhanced Rotation Angle Estimation using Trapped Ions. Phys. Rev. Lett. 2001, 86, 5870–5873. doi:10.1103/PhysRevLett.86.5870.
   PubMed Web of Science ®Google Scholar
• Leibfried, D.; DeMarco, B.; Meyer, V.; Lucas, D.; Barrett, M.; Britton, J.; Itano, W.M.; Jelenkovic, B.; Langer, C.; Rosenband, T.; Wineland, D.J. Experimental Demonstration of a Robust, High-fidelity Geometric Two Ion-qubit Phase Gate. Nature 2003, 422, 412–415. doi:10.1038/nature01492.
   PubMed Web of Science ®Google Scholar
• Leibfried, D.; Knill, E.; Seidelin, S.; Britton, J.; Blakestad, R.B.; Chiaverini, J.; Hume, D.B.; Itano, W.M.; Jost, J.D.; Langer, C.; Ozeri, R.; Reichle, R.; Wineland, D.J. Creation of a six-atom ‘Schr\"{o}dinger cat’ state. Nature 2005, 438, 639–642. doi:10.1038/nature04251.
   PubMed Web of Science ®Google Scholar
• Benhelm, J.; Kirchmair, G.; Roos, C.F.; Blatt, R. Towards Fault-tolerant Quantum Computing with Trapped Ions. Nat. Phys. 2008, 4, 463–466. doi:10.1038/nphys961.
   Web of Science ®Google Scholar
• Friedenauer, A.; Schmitz, H.; Glueckert, J.T.; Porras, D.; Schaetz, T. Simulating a Quantum Magnet with Trapped Ions. Nat. Phys. 2008, 4, 757–761. doi:10.1038/nphys1032.
   Web of Science ®Google Scholar
• Kim, K.; Chang, M.S.; Korenblit, S.; Islam, R.; Edwards, E.E.; Freericks, J.K.; Lin, G.D.; Duan, L.M.; Monroe, C. Quantum Simulation of Frustrated Ising Spins with Trapped Ions. Nature 2010, 465, 590–593. doi:10.1038/nature09071.
   PubMed Web of Science ®Google Scholar
• Monz, T.; Schindler, P.; Barreiro, J.T.; Chwalla, M.; Nigg, D.; Coish, W.A.; Harlander, M.; Hänsel, W.; Hennrich, M.; Blatt, R. 14-Qubit Entanglement: Creation and Coherence. Phys. Rev. Lett. 2011, 106, 130506. doi:10.1103/PhysRevLett.106.130506.
   PubMed Web of Science ®Google Scholar
• Ospelkaus, C.; Warring, U.; Colombe, Y.; Brown, K.R.; Amini, J.M.; Leibfried, D.; Wineland, D.J. Microwave Quantum Logic Gates for Trapped Ions. Nature 2011, 476, 181–184.
   PubMed Web of Science ®Google Scholar
• Khromova, A.; Piltz, C.; Scharfenberger, B.; Gloger, T.F.; Johanning, M.; Varón, A.F.; Wunderlich, C. Designer Spin Pseudomolecule Implemented with Trapped Ions in a Magnetic Gradient. Phys. Rev. Lett. 2012, 108, 220502. doi:10.1103/PhysRevLett.108.220502.
   PubMed Web of Science ®Google Scholar
• Weidt, S.; Randall, J.; Webster, S.C.; Lake, K.; Webb, A.E.; Cohen, I.; Navickas, T.; Lekitsch, B.; Retzker, A.; Hensinger, W.K. Trapped-ion Quantum Logic with Global Radiation Fields. Phys. Rev. Lett. 2016, 117, 220501. doi:10.1103/PhysRevLett.117.220501.
   PubMed Web of Science ®Google Scholar
• Harty, T.P.; Sepiol, M.A.; Allcock, D.T.C.; Ballance, C.J.; Tarlton, J.E.; Lucas, D.M. High-Fidelity Trapped-ion Quantum Logic using Near-field Microwaves. Phys. Rev. Lett. 2016, 117, 140501. doi:10.1103/PhysRevLett.117.140501.
   PubMed Web of Science ®Google Scholar
• Ballance, C.J.; Harty, T.P.; Linke, N.M.; Sepiol, M.A.; Lucas, D.M. High-fidelity Quantum Logic Gates using Trapped-ion Hyperfine Qubits. Phys. Rev. Lett. 2016, 117, 060504.
   PubMed Web of Science ®Google Scholar
• Gaebler, J.P.; Tan, T.R.; Lin, Y.; Wan, Y.; Bowler, R.; Keith, A.C.; Glancy, S.; Coakley, K.; Knill, E.; Leibfried, D.; Wineland, D.J. High-fidelity Universal Gate Set for 9Be+ Ion Qubits. Phys. Rev. Lett. 2016, 117, 060505. doi:10.1103/PhysRevLett.117.060505.
   PubMed Web of Science ®Google Scholar
• Heydon, A. An Introduction to Circuit Complexity and a Guide to Haestad’s proof, 2005. http://repository.cmu.edu/compsci.
   Google Scholar
• Hoyer, P.; Spalek, R. Quantum Fan-out is Powerful.. Theory Comput. 2005, 1, 83–101.
   PubMedGoogle Scholar
• Nielsen, M.A.; Chuang, I.L. Quantum Computation and Quantum Information10th anniversary edition; Cambridege University Press, Cambridge, 2010.
   Google Scholar
• Zeng, B.; Zhou, D.L.; You, L. Measuring the Parity of an N-qubit State. Phys. Rev. Lett. 2005, 95, 110502doi:10.1103/PhysRevLett.95.110502.
   PubMed Web of Science ®Google Scholar
• Wineland, D.J.; Monroe, C.; Itano, W.M.; Leibfried, D.; King, B.E.; Meekhof, D.M. Experimental Issues in Coherent Quantum-state Manipulation of Trapped Atomic Ions. J. Res. Natl. Inst. Stand. Technol. 1998, 103, 259–328.
   PubMed Web of Science ®Google Scholar
• Kielpinski, D.; Monroe, C.; Wineland, D.J. Architecture for a Large-scale Ion-trap Quantum Computer. Nature 2002, 417, 709–711. doi:10.1038/nature00784.
   PubMed Web of Science ®Google Scholar
• Nebendahl, V.; Häffner, H.; Roos, C.F. Optimal Control of Entangling Operations for Trapped-ion Quantum Computing. Phys. Rev. A 2009, 79, 012312. doi:10.1103/PhysRevA.79.012312.
   Web of Science ®Google Scholar
• Linke, N.M.; Maslov, D.; Roetteler, M.; Debnath, S.; Figgatt, C.; Landsman, K.A.; Wright, K.; Monroe, C. Experimental Comparison of Two Quantum Computing Architectures. Proc. Nat. Acad. Sci. 2017, 114, 3305–3310.
   PubMed Web of Science ®Google Scholar