Rolling quantum dice with a superconducting qubit

© 2014 American Physical Society. One of the key challenges in quantum information is coherently manipulating the quantum state. However, it is an outstanding question whether control can be realized with low error. Only gates from the Clifford group - containing π, π/2, and Hadamard gates - have been characterized with high accuracy. Here, we show how the Platonic solids enable implementing and characterizing larger gate sets. We find that all gates can be implemented with low error. The results fundamentally imply arbitrary manipulation of the quantum state can be realized with high precision, providing practical possibilities for designing efficient quantum algorithms.

[1]  A. Kitaev.  Quantum computations: algorithms and error correction , 1997 .

[2]  G. Vetrovec.  DES , 2021, Encyclopedia of Systems and Control.

[3]  J. Emerson,et al.  Scalable noise estimation with random unitary operators , 2005, quant-ph/0503243.

[4]  Christoph Dankert,et al.  Exact and Approximate Unitary 2-Designs: Constructions and Applications , 2006, quant-ph/0606161.

[5]  These authors contributed equally to this work. , 2007 .

[6]  D. Gross,et al.  Evenly distributed unitaries: On the structure of unitary designs , 2006, quant-ph/0611002.

[7]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[8]  Christoph Dankert,et al.  Exact and approximate unitary 2-designs and their application to fidelity estimation , 2009 .

[9]  J. P. Home,et al.  Realization of a programmable two-qubit quantum processor , 2009, 0908.3031.

[10]  R. Laflamme,et al.  Randomized benchmarking of single- and multi-qubit control in liquid-state NMR quantum information processing , 2008, 0808.3973.

[11]  Aidan Roy,et al.  Unitary designs and codes , 2008, Des. Codes Cryptogr..

[12]  S. Girvin,et al.  Implementing optimal control pulse shaping for improved single-qubit gates , 2010, 1005.1279.

[13]  Erik Lucero,et al.  Reduced phase error through optimized control of a superconducting qubit , 2010, 1007.1690.

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

[15]  B. Lanyon,et al.  Universal Digital Quantum Simulation with Trapped Ions , 2011, Science.

[16]  Joseph Emerson,et al.  Scalable and robust randomized benchmarking of quantum processes. , 2010, Physical review letters.

[17]  M Steffen,et al.  Efficient measurement of quantum gate error by interleaved randomized benchmarking. , 2012, Physical review letters.

[18]  Jay M. Gambetta,et al.  Characterizing Quantum Gates via Randomized Benchmarking , 2011, 1109.6887.

[19]  Yasunobu Nakamura,et al.  Improving quantum gate fidelities by using a qubit to measure microwave pulse distortions. , 2012, Physical review letters.

[20]  Shelby Kimmel,et al.  Robust Extraction of Tomographic Information via Randomized Benchmarking , 2013, 1306.2348.

[21]  Jay M. Gambetta,et al.  Process verification of two-qubit quantum gates by randomized benchmarking , 2012, 1210.7011.

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

[23]  Andrew W. Cross,et al.  Investigating the limits of randomized benchmarking protocols , 2013, 1308.2928.

[24]  R. Barends,et al.  Superconducting quantum circuits at the surface code threshold for fault tolerance , 2014, Nature.

[25]  A N Cleland,et al.  Optimal quantum control using randomized benchmarking. , 2014, Physical review letters.

[26]  N. Linke,et al.  High-Fidelity Preparation, Gates, Memory, and Readout of a Trapped-Ion Quantum Bit. , 2014, Physical review letters.

[27]  Matthew B. Hastings,et al.  Improving quantum algorithms for quantum chemistry , 2014, Quantum Inf. Comput..

[28]  Neil J. Ross,et al.  Optimal ancilla-free Clifford+T approximation of z-rotations , 2014, Quantum Inf. Comput..