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With qubit measurement and control fidelities above the threshold of fault-tolerance, much attention is moving towards the daunting task of scaling up the number of physical qubits to the large numbers needed for fault tolerant quantum computing. Here, quantum dot based spin qubits may offer significant advantages due to their potential for high densities, all-electrical operation, and integration onto an industrial platform. In this system, the initialisation, readout, single- and two-qubit gates have been demonstrated in various qubit representations. However, as seen with other small scale quantum computer demonstrations, combining these elements leads to new challenges involving qubit crosstalk, state leakage, calibration, and control hardware which provide invaluable insight towards scaling up. Here we address these challenges and demonstrate a programmable two-qubit quantum processor in silicon by performing both the Deutsch-Josza and the Grover search algorithms. In addition, we characterise the entanglement in our processor through quantum state tomography of Bell states measuring state fidelities between 85-89% and concurrences between 73-80%. These results pave the way for larger scale quantum computers using spins confined to quantum dots.

The valley degree of freedom is intrinsic to spin qubits in Si/SiGe quantum dots. It has been viewed alternately as a hazard, especially when the lowest valley-orbit splitting is small compared to the thermal energy, or as an asset, most prominently in proposals to use the valley degree of freedom itself as a qubit. Here we present experiments in which microwave electric field driving induces transitions between both valley-orbit and spin states. We show that this system is highly nonlinear and can be understood through the use of dressed photon-orbital states, enabling a unified understanding of the six microwave resonance lines we observe. Some of these resonances are inter-valley spin transitions that arise from a non-adiabatic process in which both the valley and the spin degree of freedom are excited simultaneously. For these transitions, involving a change in valley-orbit state, we find a tenfold increase in sensitivity to electric fields and electrical noise compared to pure spin transitions, strongly reducing the phase coherence when changes in valley-orbit index are incurred. In contrast to this non-adiabatic transition, the pure spin transitions, whether arising from harmonic or subharmonic generation, are shown to be adiabatic in the orbital sector. The non-linearity of the system is most strikingly manifest in the observation of a dynamical anti-crossing between a spin-flip, inter-valley transition and a three-photon transition enabled by the strong nonlinearity we find in this seemly simple system., Comment: 23 pages, 11 figures, supplementary material included

The gate fidelity and the coherence time of a qubit are important benchmarks for quantum computation. We construct a qubit using a single electron spin in a Si/SiGe quantum dot and control it electrically via an artificial spin-orbit field from a micromagnet. We measure an average single-qubit gate fidelity of $\approx$ 99$\%$ using randomized benchmarking, which is consistent with dephasing from the slowly evolving nuclear spins in substrate. The coherence time measured using dynamical decoupling extends up to $\approx$ 400 $\mu$s for 128 decoupling pulses, with no sign of saturation. We find evidence that the coherence time is limited by noise in the 10 kHz $-$ 1 MHz range, possibly because charge noise affecting the spin via the micromagnet gradient. This work shows that an electron spin in a Si/SiGe quantum dot is a good candidate for quantum information processing as well as for a quantum memory, even without isotopic purification.

We demonstrate coherent driving of a single electron spin using second harmonic excitation in a Si/SiGe quantum dot. Our estimates suggest that the anharmonic dot confining potential combined with a gradient in the transverse magnetic field dominates the second harmonic response. As expected, the Rabi frequency depends quadratically on the driving amplitude and the periodicity with respect to the phase of the drive is twice that of the fundamental harmonic. The maximum Rabi frequency observed for the second harmonic is just a factor of two lower than that achieved for the first harmonic when driving at the same power. Combined with the lower demands on microwave circuitry when operating at half the qubit frequency, these observations indicate that second harmonic driving can be a useful technique for future quantum computation architectures., Comment: 9 pages, 9 figures

We report that the electron spin relaxation time, T1, in a GaAs quantum dot with a spin-1/2 ground state has a 180 degree periodicity in the orientation of the in-plane magnetic field. This periodicity has been predicted for circular dots as due to the interplay of Rashba and Dresselhaus spin orbit contributions. Different from this prediction, we find that the extrema in the T1 do not occur when the magnetic field is along the [110] and [1-10] crystallographic directions. This deviation is attributed to an elliptical dot confining potential. The T1 varies by more than an order of magnitude when rotating a 3 Tesla field, reaching about 80 ms for the magic angle. We infer from the data that in our device the sign of the Rashba and Dresselhaus constants are opposite., Comment: 8 pages, 8 figures

Nanofabricated quantum bits permit large-scale integration but usually suffer from short coherence times due to interactions with their solid-state environment. The outstanding challenge is to engineer the environment so that it minimally affects the qubit, but still allows qubit control and scalability. Here we demonstrate a long-lived single-electron spin qubit in a Si/SiGe quantum dot with all-electrical two-axis control. The spin is driven by resonant microwave electric fields in a transverse magnetic field gradient from a local micromagnet, and the spin state is read out in single-shot mode. Electron spin resonance occurs at two closely spaced frequencies, which we attribute to two valley states. Thanks to the weak hyperfine coupling in silicon, Ramsey and Hahn echo decay timescales of 1us and 40us, respectively, are observed. This is almost two orders of magnitude longer than the intrinsic timescales in III-V quantum dots, while gate operation times are comparable to those achieved in GaAs. This places the single-qubit rotations in the fault-tolerant regime and strongly raises the prospects of quantum information processing based on quantum dots., Comment: submitted 26th February 2014

We report transport measurements on a Si/SiGe quantum dot subject to microwave excitation via an on-chip antenna. The response shows signatures of photon-assisted tunneling and only a small effect on charge stability. We also explore the use of a d.c. current applied to the antenna for generating tunable, local magnetic field gradients and put bounds on the achievable field gradients, limited by heating of the reservoirs.