Entanglement Generation in Superconducting Qubits Using Holonomic Operations

We investigate a non-adiabatic holonomic operation that enables us to entangle two fixed-frequency superconducting transmon qubits attached to a common bus resonator. Two coherent microwave tones are applied simultaneously to the two qubits and drive transitions between the first excited resonator state and the second excited state of each qubit. The cyclic evolution within this effective 3-level $\Lambda$-system gives rise to a holonomic operation entangling the two qubits. Two-qubit states with 95\% fidelity, limited mainly by charge-noise of the current device, are created within $213~\rm{ns}$. This scheme is a step toward implementing a SWAP-type gate directly in an all-microwave controlled hardware platform. By extending the available set of two-qubit operations in the fixed-frequency qubit architecture, the proposed scheme may find applications in near-term quantum applications using variational algorithms to efficiently create problem-specific trial states.

[1]  P. Coveney,et al.  Scalable Quantum Simulation of Molecular Energies , 2015, 1512.06860.

[2]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[3]  Jay M. Gambetta,et al.  Improved superconducting qubit coherence using titanium nitride , 2013, 1303.4071.

[4]  Effect of noise on geometric logic gates for quantum computation , 2001, quant-ph/0105006.

[5]  S. Filipp,et al.  Control and tomography of a three level superconducting artificial atom. , 2010, Physical review letters.

[6]  Erik Lucero,et al.  Surface loss simulations of superconducting coplanar waveguide resonators , 2011, 1107.4698.

[7]  D. Tannor,et al.  Tunable, Flexible, and Efficient Optimization of Control Pulses for Practical Qubits. , 2018, Physical review letters.

[8]  Jiangfeng Du,et al.  NMR implementation of a molecular hydrogen quantum simulation with adiabatic state preparation. , 2010, Physical review letters.

[9]  Christiane P. Koch,et al.  Training Schrödinger’s cat: quantum optimal control , 2015, 1508.00442.

[10]  Franco Nori,et al.  Comparison of the sensitivity to systematic errors between nonadiabatic non-Abelian geometric gates and their dynamical counterparts , 2016, 1603.08061.

[11]  A. A. Abdumalikov,et al.  Measurement of geometric dephasing using a superconducting qubit , 2015, Nature Communications.

[12]  A. A. Abdumalikov,et al.  Measurement of a vacuum-induced geometric phase , 2016, Science Advances.

[13]  A. Shnirman,et al.  Geometric quantum gates with superconducting qubits , 2011, 1104.0159.

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

[15]  J. Gambetta,et al.  Procedure for systematically tuning up cross-talk in the cross-resonance gate , 2016, 1603.04821.

[16]  Jens Koch,et al.  Suppressing Charge Noise Decoherence in Superconducting Charge Qubits , 2007, 0712.3581.

[17]  J. Gambetta,et al.  Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets , 2017, Nature.

[18]  S. Berger,et al.  Exploring the effect of noise on the Berry phase , 2013, 1302.3305.

[19]  Stefan W. Hell,et al.  Room temperature high-fidelity holonomic single-qubit gate on a solid-state spin , 2014, Nature Communications.

[20]  C. Zu,et al.  Experimental realization of universal geometric quantum gates with solid-state spins , 2014, Nature.

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

[22]  R. J. Schoelkopf,et al.  Observation of Berry's Phase in a Solid-State Qubit , 2007, Science.

[23]  Berry phase in a nonisolated system. , 2002, Physical review letters.

[24]  Gorjan Alagic,et al.  #p , 2019, Quantum information & computation.

[25]  P. Alam.  ‘G’ , 2021, Composites Engineering: An A–Z Guide.

[26]  S. Berger,et al.  Microwave-Controlled Generation of Shaped Single Photons in Circuit Quantum Electrodynamics , 2013, 1308.4094.

[27]  Hideo Kosaka,et al.  Optical holonomic single quantum gates with a geometric spin under a zero field , 2017 .

[28]  P Geltenbort,et al.  Experimental demonstration of the stability of Berry's phase for a spin-1/2 particle. , 2008, Physical review letters.

[29]  B. Lanyon,et al.  Towards quantum chemistry on a quantum computer. , 2009, Nature chemistry.

[30]  Ivano Tavernelli,et al.  Optimizing qubit resources for quantum chemistry simulations in second quantization on a quantum computer , 2015, 1510.04048.

[31]  V. O. Shkolnikov,et al.  Holonomic Quantum Control by Coherent Optical Excitation in Diamond. , 2017, Physical review letters.

[32]  Sophie Shermer.  Training Schrödinger’s cat: quantum optimal control , 2015 .

[33]  P. Alam.  ‘A’ , 2021, Composites Engineering: An A–Z Guide.

[34]  Tao Chen,et al.  Single-Loop Realization of Arbitrary Nonadiabatic Holonomic Single-Qubit Quantum Gates in a Superconducting Circuit. , 2018, Physical review letters.

[35]  Franco Nori,et al.  QuTiP 2: A Python framework for the dynamics of open quantum systems , 2012, Comput. Phys. Commun..

[36]  D J Egger,et al.  Adaptive hybrid optimal quantum control for imprecisely characterized systems. , 2014, Physical review letters.

[37]  D. M. Tong,et al.  Robustness of nonadiabatic holonomic gates , 2012, 1204.5144.

[38]  Z. D. Wang,et al.  Implementing universal nonadiabatic holonomic quantum gates with transmons , 2017, 1710.03141.

[39]  E. Sjoqvist.  Geometric phases in quantum information , 2015, 1503.04847.

[40]  Alexandre Blais,et al.  Quantum information processing with circuit quantum electrodynamics , 2007 .

[41]  Chad Rigetti,et al.  Fully microwave-tunable universal gates in superconducting qubits with linear couplings and fixed transition frequencies , 2010 .

[42]  P. Alam.  ‘L’ , 2021, Composites Engineering: An A–Z Guide.

[43]  R. Laflamme,et al.  Geometric phase with nonunitary evolution in the presence of a quantum critical bath. , 2010, Physical review letters.

[44]  S. Berger,et al.  Microwave-Induced Amplitude and Phase Tunable Qubit-Resonator Coupling in Circuit Quantum Electrodynamics , 2015, 1502.03692.

[45]  W. Oliver,et al.  Materials in superconducting quantum bits , 2013 .

[46]  Yang Liu,et al.  Experimental realization of single-shot nonadiabatic holonomic gates in nuclear spins , 2017, 1703.10348.

[47]  Ivano Tavernelli,et al.  Quantum chemistry algorithms for efficient quantum computing , 2018 .

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

[49]  Jonathan Carter,et al.  Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm , 2018 .

[50]  Ivano Tavernelli,et al.  Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions , 2018, Physical Review A.

[51]  J. Gambetta,et al.  Efficient Z gates for quantum computing , 2016, 1612.00858.

[52]  Geometric phase in open systems. , 2003, Physical review letters.

[53]  P. Alam.  ‘T’ , 2021, Composites Engineering: An A–Z Guide.

[54]  Fleischhauer,et al.  Propagation of laser pulses and coherent population transfer in dissipative three-level systems: An adiabatic dressed-state picture. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[55]  S. Berger,et al.  Experimental realization of non-Abelian non-adiabatic geometric gates , 2013, Nature.

[56]  Alán Aspuru-Guzik,et al.  A variational eigenvalue solver on a photonic quantum processor , 2013, Nature Communications.

[57]  G. Paraoanu,et al.  Experimental state control by fast non-Abelian holonomic gates with a superconducting qutrit , 2018, 1804.01759.

[58]  H. Riemann,et al.  Geometric phase gates with adiabatic control in electron spin resonance , 2012, 1208.0555.

[59]  Guilu Long,et al.  Experimental realization of nonadiabatic holonomic quantum computation. , 2013, Physical review letters.

[60]  Luigi Frunzio,et al.  Surface participation and dielectric loss in superconducting qubits , 2015, 1509.01854.

[61]  R. Schoelkopf,et al.  Superconducting Circuits for Quantum Information: An Outlook , 2013, Science.

[62]  F. K. Wilhelm,et al.  Optimized controlled-Z gates for two superconducting qubits coupled through a resonator , 2013, 1306.6894.

[63]  Antonio-José Almeida,et al.  NAT , 2019, Springer Reference Medizin.

[64]  Gabriele De Chiara,et al.  Berry phase for a spin 1/2 particle in a classical fluctuating field. , 2003, Physical review letters.

[65]  P. Alam.  ‘Z’ , 2021, Composites Engineering: An A–Z Guide.

[66]  Paolo Zanardi,et al.  Robustness of non-Abelian holonomic quantum gates against parametric noise , 2004 .

[67]  Paolo Zanardi,et al.  Holonomic quantum computation , 1999 .

[68]  D. M. Tong,et al.  Non-adiabatic holonomic quantum computation , 2011, 1107.5127.

[69]  H. Kosaka,et al.  Universal holonomic single quantum gates over a geometric spin with phase-modulated polarized light. , 2018, Optics letters.