Hidden two-qubit dynamics of a four-level Josephson circuit

Multi-level control of quantum coherence exponentially reduces communication and computation resources required for a variety of applications of quantum information science. However, it also introduces complex dynamics to be understood and controlled. These dynamics can be simplified and made intuitive by employing group theory to visualize certain four-level dynamics in a 'Bell frame' comprising an effective pair of uncoupled two-level qubits. We demonstrate control of a Josephson phase qudit with a single multi-tone excitation, achieving successive population inversions between the first and third levels and highlighting constraints imposed by the two-qubit representation. Furthermore, the finite anharmonicity of our system results in a rich dynamical evolution, where the two Bell-frame qubits undergo entangling-disentangling oscillations in time, explained by a Cartan gate decomposition representation. The Bell frame constitutes a promising tool for control of multi-level quantum systems, providing an intuitive clarity to complex dynamics.

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

[2]  Luigi Frunzio,et al.  Realization of three-qubit quantum error correction with superconducting circuits , 2011, Nature.

[3]  V. Shumeiko,et al.  Quantum bits with Josephson junctions (Review Article) , 2007 .

[4]  Archil Avaliani,et al.  Quantum Computers , 2004, ArXiv.

[5]  King,et al.  Demonstration of a fundamental quantum logic gate. , 1995, Physical review letters.

[6]  J. Cole,et al.  Multiphoton spectroscopy of a hybrid quantum system , 2010, 1005.0773.

[7]  J. Cirac,et al.  Quantum Computations with Cold Trapped Ions. , 1995, Physical review letters.

[8]  D. DiVincenzo,et al.  The Physical Implementation of Quantum Computation , 2000, quant-ph/0002077.

[9]  Erik Lucero,et al.  Emulation of a Quantum Spin with a Superconducting Phase Qudit , 2009, Science.

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

[11]  John M Martinis,et al.  Decoherence in josephson phase qubits from junction resonators. , 2004, Physical review letters.

[12]  Charles H. Bennett,et al.  Concentrating partial entanglement by local operations. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[13]  Barenco,et al.  Elementary gates for quantum computation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[14]  J. Cirac,et al.  Optimal creation of entanglement using a two-qubit gate , 2000, quant-ph/0011050.

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

[16]  Y. Silberberg,et al.  Pythagorean coupling: Complete population transfer in a four-state system , 2011 .

[17]  D. Deutsch.  Quantum computational networks , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[18]  Lloyd,et al.  Almost any quantum logic gate is universal. , 1995, Physical review letters.

[19]  Pedram Khalili Amiri,et al.  Quantum computers , 2003 .

[20]  John M. Martinis,et al.  Superconducting phase qubits , 2009, Quantum Inf. Process..

[21]  J. Martinis,et al.  Direct Wigner tomography of a superconducting anharmonic oscillator. , 2012, Physical review letters.

[22]  R. Barends,et al.  Coherent Josephson qubit suitable for scalable quantum integrated circuits. , 2013, Physical review letters.

[23]  Todd A. Brun,et al.  Quantum Computing , 2011, Computer Science, The Hardware, Software and Heart of It.

[24]  B. Garside.  Optical Resonance and Two-level Atoms , 1975 .

[25]  DiVincenzo.  Two-bit gates are universal for quantum computation. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[26]  I. Barth,et al.  Quantum and classical chirps in an anharmonic oscillator. , 2011, Physical review letters.

[27]  I. Chuang,et al.  Quantum Computation and Quantum Information: Introduction to the Tenth Anniversary Edition , 2010 .