Spin-orbit coupling and operation of multivalley spin qubits

Spin qubits composed of either one or three electrons are realized in a quantum dot formed at a Si/SiO_2-interface in isotopically enriched silicon. Using pulsed electron spin resonance, we perform coherent control of both types of qubits, addressing them via an electric field dependent g-factor. We perform randomized benchmarking and find that both qubits can be operated with high fidelity. Surprisingly, we find that the g-factors of the one-electron and three-electron qubits have an approximately linear but opposite dependence as a function of the applied dc electric field. We develop a theory to explain this g-factor behavior based on the spin-valley coupling that results from the sharp interface. The outer "shell" electron in the three-electron qubit exists in the higher of the two available conduction-band valley states, in contrast with the one-electron case, where the electron is in the lower valley. We formulate a modified effective mass theory and propose that inter-valley spin-flip tunneling dominates over intra-valley spin-flips in this system, leading to a direct correlation between the spin-orbit coupling parameters and the g-factors in the two valleys. In addition to offering all-electrical tuning for single-qubit gates, the g-factor physics revealed here for one-electron and three-electron qubits offers potential opportunities for new qubit control approaches.

[1]  A. Dzurak,et al.  Charge offset stability in Si single electron devices with Al gates , 2014, Nanotechnology.

[2]  Mark Friesen,et al.  Electrical control of a long-lived spin qubit in a Si/SiGe quantum dot. , 2014, Nature nanotechnology.

[3]  F. J. Ohkawa.  Electric break-through in an inversion layer: Exactly solvable model , 1978 .

[4]  Isotope engineering of silicon and diamond for quantum computing and sensing applications , 2014, 1410.3922.

[5]  E. Knill,et al.  Randomized Benchmarking of Quantum Gates , 2007, 0707.0963.

[6]  Damon Afkari,et al.  ? ? ? ? ? ? ? ? ? ? ? ? ? 30 ? ? ? ? ? ? ? ? ? ? ? ? ? ? , 2011 .

[7]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[8]  F. Stern,et al.  Electronic properties of two-dimensional systems , 1982 .

[9]  S. N. Coppersmith,et al.  Theory of valley-orbit coupling in a Si/SiGe quantum dot , 2009, 0902.0777.

[10]  J. P. Dehollain,et al.  A two-qubit logic gate in silicon , 2014, Nature.

[11]  M. Veldhorst,et al.  Nonexponential fidelity decay in randomized benchmarking with low-frequency noise , 2015, 1502.05119.

[12]  P. Voisin,et al.  Electric field effect on electron spin splitting in SiGe/Si quantum wells , 2007, 0712.1955.

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

[14]  D. DiVincenzo,et al.  Validity of the single-particle description and charge noise resilience for multielectron quantum dots , 2015, 1502.03357.

[15]  Andrew S. Dzurak,et al.  A single-atom electron spin qubit in silicon , 2012, Nature.

[16]  Michelle Y. Simmons,et al.  Silicon quantum electronics , 2012, 1206.5202.

[17]  M. Mariantoni,et al.  Surface codes: Towards practical large-scale quantum computation , 2012, 1208.0928.

[18]  Gerhard Klimeck,et al.  Spin-valley lifetimes in a silicon quantum dot with tunable valley splitting , 2013, Nature Communications.

[19]  Adele E. Schmitz,et al.  Coherent singlet-triplet oscillations in a silicon-based double quantum dot , 2012, Nature.

[20]  S. Sarma,et al.  Physical mechanisms for interface-mediated intervalley coupling in Si , 2009, 0901.4702.

[21]  J. P. Dehollain,et al.  An addressable quantum dot qubit with fault-tolerant control-fidelity. , 2014, Nature nanotechnology.

[22]  Gerhard Klimeck,et al.  Electrically controlling single-spin qubits in a continuous microwave field , 2015, Science Advances.

[23]  Vladimir A. Volkov,et al.  Boundary conditions, energy spectrum, and optical transitions of electrons in bounded narrow gap crystals , 1979 .

[24]  E. Ivchenko,et al.  Spin splitting in symmetrical SiGe quantum wells , 2003, cond-mat/0310200.

[25]  E. Ivchenko,et al.  Electron g factor in one- and zero-dimensional semiconductor nanostructures , 1998 .

[26]  Zhan Shi,et al.  Quantum control and process tomography of a semiconductor quantum dot hybrid qubit , 2014, Nature.

[27]  S. Sarma,et al.  Quantum dot spin qubits in silicon: Multivalley physics , 2010, 1001.5040.

[28]  A. Dzurak,et al.  Gate-defined quantum dots in intrinsic silicon. , 2007, Nano letters.

[29]  Fedor T. Vasko,et al.  Spin splitting in the spectrum of two-dimensional electrons due to the surface potential , 1979 .

[30]  P. Kam,et al.  : 4 , 1898, You Can Cross the Massacre on Foot.