Quantum-control approach to realizing a Toffoli gate in circuit QED

We study the realization of a Toffoli gate with superconducting qubits in a circuit-quantum-electrodynamics setup using quantum-control methods. Starting with optimized piecewise-constant control fields acting on all qubits and typical strengths of XY-type coupling between the qubits, we demonstrate that the optimal gate fidelities are affected only slightly by a ``low-pass`` filtering of these fields with the typical cutoff frequencies of microwave driving. Restricting ourselves to the range of control-field amplitudes for which the leakage to the noncomputational states of a physical qubit is heavily suppressed, we theoretically predict that in the absence of decoherence and leakage, within 75 ns a Toffoli gate can be realized with intrinsic fidelities higher than 90% while fidelities above 99% can be reached in about 140 ns.

[1]  Clarke,et al.  Energy-level quantization in the zero-voltage state of a current-biased Josephson junction. , 1985, Physical review letters.

[2]  William H. Press,et al.  Numerical recipes in Fortran 77 and Fortran 90 : the art of scientific and parallel computing , 1996 .

[3]  Jens Siewert,et al.  Fidelity and leakage of Josephson qubits , 1999 .

[4]  Y. Makhlin,et al.  Quantum-state engineering with Josephson-junction devices , 2000, cond-mat/0011269.

[5]  John M. Martinis,et al.  Accurate Control of Josephson Phase Qubits , 2003 .

[6]  S. Girvin,et al.  Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation , 2004, cond-mat/0402216.

[7]  S. Girvin,et al.  Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics , 2004, Nature.

[8]  F. Nori,et al.  Superconducting Circuits and Quantum Information , 2005, quant-ph/0601121.

[9]  Jun Zhang,et al.  Generation of quantum logic operations from physical Hamiltonians (13 pages) , 2005 .

[10]  N. Mermin.  Quantum Computer Science: An Introduction , 2007 .

[11]  Tommaso Calarco,et al.  Robust optimal quantum gates for Josephson charge qubits. , 2007, Physical review letters.

[12]  Andrei Galiautdinov.  Generation of high-fidelity controlled-NOT logic gates by coupled superconducting qubits , 2007 .

[13]  S. Girvin,et al.  Charge-insensitive qubit design derived from the Cooper pair box , 2007, cond-mat/0703002.

[14]  D. D’Alessandro.  Introduction to Quantum Control and Dynamics , 2007 .

[15]  Jens Koch,et al.  Coupling superconducting qubits via a cavity bus , 2007, Nature.

[16]  J. Clarke,et al.  Superconducting quantum bits , 2008, Nature.

[17]  Sonia G. Schirmer,et al.  Global controllability with a single local actuator , 2008 .

[18]  Marco Barbieri,et al.  Simplifying quantum logic using higher-dimensional Hilbert spaces , 2009 .

[19]  L. DiCarlo,et al.  Demonstration of two-qubit algorithms with a superconducting quantum processor , 2009, Nature.

[20]  John M. Martinis,et al.  Quantum logic with weakly coupled qubits , 2009, 0906.5209.

[21]  S. Lloyd,et al.  Constructing two-qubit gates with minimal couplings , 2009 .

[22]  T. Monz,et al.  Realization of the quantum Toffoli gate with trapped ions. , 2008, Physical review letters.

[23]  P. Rebentrost,et al.  Optimal control of a leaking qubit , 2008, 0808.2680.

[24]  Vittorio Giovannetti,et al.  Local controllability of quantum networks , 2009 .

[25]  J M Gambetta,et al.  Simple pulses for elimination of leakage in weakly nonlinear qubits. , 2009, Physical review letters.

[26]  S. Filipp,et al.  Multimode mediated qubit-qubit coupling and dark-state symmetries in circuit quantum electrodynamics , 2010, 1011.3732.

[27]  Daniel Burgarth,et al.  Local quantum control of Heisenberg spin chains , 2010, 1007.2572.

[28]  S. J. Glaser,et al.  Optimal control of circuit quantum electrodynamics in one and two dimensions , 2009, 0911.4657.

[29]  Luigi Frunzio,et al.  Optimized driving of superconducting artificial atoms for improved single-qubit gates , 2010 .

[30]  Michael R. Geller,et al.  Controlled-NOT gate with weakly coupled qubits: Dependence of fidelity on the form of interaction , 2010, 1003.2718.

[31]  S. Girvin,et al.  Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. , 2011, Physical review letters.

[32]  A. Gruslys,et al.  Comparing, optimizing, and benchmarking quantum-control algorithms in a unifying programming framework , 2010, 1011.4874.

[33]  Erik Lucero,et al.  Implementing the Quantum von Neumann Architecture with Superconducting Circuits , 2011, Science.

[34]  F. Wellstood,et al.  Decoupling a Cooper-pair box to enhance the lifetime to 0.2 ms. , 2011, Physical review letters.

[35]  J. M. Gambetta,et al.  Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator , 2010, 1011.1949.

[36]  R. Heule,et al.  Controlling qubit arrays with anisotropic XXZ Heisenberg interaction by acting on a single qubit , 2010, 1010.5715.

[37]  Marcus P. da Silva,et al.  Implementation of a Toffoli gate with superconducting circuits , 2011, Nature.