Now that it is possible to achieve measurement and control fidelities for individual quantum bits (qubits) above the threshold for fault tolerance, attention is moving towards the difficult task of scaling up the number of physical qubits to the large numbers that are needed for fault-tolerant quantum computing. In this context, quantum-dot-based spin qubits could have substantial advantages over other types of qubit owing to their potential for all-electrical operation and ability to be integrated at high density onto an industrial platform. Initialization, readout and single- and two-qubit gates have been demonstrated in various quantum-dot-based qubit representations. However, as seen with small-scale demonstrations of quantum computers using other types of qubit, combining these elements leads to challenges related to qubit crosstalk, state leakage, calibration and control hardware. Here we overcome these challenges by using carefully designed control techniques to demonstrate a programmable two-qubit quantum processor in a silicon device that can perform the Deutsch-Josza algorithm and the Grover search algorithm-canonical examples of quantum algorithms that outperform their classical analogues. We characterize the entanglement in our processor by using quantum-state tomography of Bell states, measuring state fidelities of 85-89 per cent and concurrences of 73-82 per cent. These results pave the way for larger-scale quantum computers that use spins confined to quantum dots.

Nanofabricated quantum bits permit large-scale integration but usually suffer from short coherence times due to interactions with their solid-state environment 1 . 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 2,3 , and the spin state is read out in single-shot mode 4 . 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 s µ 1 and s µ 40 , respectively, are observed. This is almost two orders of magnitude longer than the intrinsic timescales in III-V quantum dots 5,6 , while gate operation times are comparable to those achieved in GaAs 3,7,8 . This places the single-qubit rotations in the fault-tolerant regime 9 and strongly raises the prospects of quantum information processing based on quantum dots.The proposal by Loss and DiVincenzo 10 to define quantum bits by the state of a single electron spin in a gate-defined semiconductor quantum dot has guided research for the past 15 years 7 . Most progress was made in well-controlled III-V quantum dots, where spin manipulation with two 6,11 , three 12 and four 13 dots has been realized, but gate fidelities and spin coherence times are limited by the unavoidable interaction with the fluctuating nuclear spins in the host substrate 5,6 . While the randomness of the nuclear spin bath could be mitigated to some extent by feedback techniques 14 , eliminating the nuclear spins by using group IV host materials offers the potential for extremely long electron spin coherence times that exceed one second in P impurities in bulk 28 Si 15,16 .Much effort has been made to develop stable spin qubits in quantum dots defined in carbon nanotubes 17,18 , Ge/Si core/shell nanowires 19 , Si MOSFETs 20,21 and Si/SiGe 2D electron gases 16,22,23 . However, coherent control in these group IV quantum dots is so far limited to a Si/SiGe singlet-triplet qubit with only single-axis control 23 and a carbon nanotube single-electron spin qubit, with a Hahn echo decay time of 65 ns 17 .Our device is based on an undoped Si/SiGe heterostructure with two layers of electrostatic gates (Fig. 1a). Compared to conventional, doped heterostructures, this technology strongly improves charge stability 23 . First, accumulation gates ( mV 150 a + V ) are used to induce a twodimensional electron gas (2DEG) in a 12 nm wide Si quantum well 37 nm below the surface. Second, a set of depletion gates, labelled 1-12 in Fig. 1a, is used to form a single or double quantum dot in the 2DEG, flanked by a quantum point contact and another dot intended as charge sensors. Two μm 1 -wide, 200 nm-thick, and μm 5 . 1 -long Co magnets are placed...

The strong coupling limit of cavity quantum electrodynamics (QED) implies the capability of a matter-like quantum system to coherently transform an individual excitation into a single photon within a resonant structure. This not only enables essential processes required for quantum information processing but also allows for fundamental studies of matter-light interaction. In this work we demonstrate strong coupling between the charge degree of freedom in a gate-defined GaAs double quantum dot (DQD) and a frequency-tunable high impedance resonator realized using an array of superconducting quantum interference devices (SQUIDs). In the resonant regime, we resolve the vacuum Rabi mode splitting of size 2g/2π = 238 MHz at a resonator linewidth κ/2π = 12 MHz and a DQD charge qubit dephasing rate of γ2/2π = 80 MHz extracted independently from microwave spectroscopy in the dispersive regime. Our measurements indicate a viable path towards using circuit based cavity QED for quantum information processing in semiconductor nano-structures.In the strong coupling limit, cavity QED realizes the coherent exchange of a single quantum of energy between a nonlinear quantum system with two or more energy levels, e.g. a qubit, and a single mode of a high quality cavity capable of storing individual photons [1]. The distinguishing feature of strong coupling is a coherent coupling rate g, determined by the product of the dipole moment of the multi-level system and the vacuum field of the cavity, which exceeds both the cavity mode linewidth κ, determining the photon life time, and the qubit linewidth γ 2 = γ 1 /2 + γ ϕ , set by its energy relaxation and pure dephasing rates, γ 1 and γ ϕ , respectively.The strong coupling limit of Cavity QED has been reached with a multitude of physical systems including alkali atoms [2], Rydberg atoms [3], superconducting circuits [4,5] and optical transitions in semiconductor quantum dots [6,7]. Of particular interest is the use of this concept in quantum information processing with supercondcuting circuits where it is known as circuit QED [4,8,9].Motivated by the ability to suppress the spontaneous emission of qubits beyond the free space limit [10], to perform quantum non-demolition (QND) qubit read-out [11,12], to couple distant qubits through microwave photons coherently [13,14] and to convert quantum information stored in stationary qubits to photons [15,16], research towards reaching the strong coupling limit of cavity QED is pursued for the charge and spin degrees of freedom in semiconductor nano-structures [17][18][19][20][21][22]. Recently, in parallel with the work discussed here, independent efforts to reach this goal have come to fruition with gate defined DQDs in silicon [23] and carbon nanotubes [24].The essence of our approach to reach the strong coupling limit with individual electronic charges in GaAs DQDs is rooted in the enhancement of the electric component of the vacuum fluctuations ∝ √ Z r [25] by increas-ing the resonator impedance Z r beyond the typical 50 Ω of a standard copl...

We present superconducting microwave-frequency resonators based on NbTiN nanowires. The small cross section of the nanowires minimizes vortex generation, making the resonators resilient to magnetic fields. Measured intrinsic quality factors exceed 2 × 10 5 in a 6 T in-plane magnetic field, and 3 × 10 4 in a 350 mT perpendicular magnetic field. Due to their high characteristic impedance, these resonators are expected to develop zero-point voltage fluctuations one order of magnitude larger than in standard coplanar waveguide resonators. These properties make the nanowire resonators well suited for circuit QED experiments needing strong coupling to quantum systems with small electric dipole moments and requiring a magnetic field, such as electrons in single and double quantum dots. arXiv:1511.01760v1 [cond-mat.mes-hall] 5 Nov 2015