Abstract:Single qubit rotations and two-qubit CNOT operations are crucial ingredients for universal quantum computing. While high fidelity single qubit operations have been achieved using the electron spin degree of freedom, realizing a robust CNOT gate has been a major challenge due to rapid nuclear spin dephasing and charge noise. We demonstrate an efficient resonantly-driven CNOT gate for electron spins in silicon. Our platform achieves single-qubit rotations with fidelities >99%, as verified by randomized benchmarking. Gate control of the exchange coupling allows a quantum CNOT gate to be implemented with resonant driving in ~200 ns. We use the CNOT gate to generate a Bell state with 75% fidelity, limited by quantum state readout. Our quantum dot device architecture opens the door to multi-qubit algorithms in silicon.Main Text: Gate defined semiconductor quantum dots are a powerful platform for isolating and coherently controlling single electron spins (1, 2). Silicon quantum dots can leverage state-ofthe-art industrial nanofabrication capabilities for scalability, and support some of the longest quantum coherence times measured in the solid-state (3-5). By engineering local magnetic field gradients, electron spins can be electrically controlled (6, 7) with single qubit gate fidelities exceeding 99% (8). Despite this progress, demonstrations of two-qubit gates with quantum dot spins are scarce due to technological and materials challenges (9, 10). While exchange control of spins was demonstrated as early as 2005, high fidelity exchange gates have been difficult to achieve due to nuclear spin dephasing and charge noise (10, 11). A demonstration of an efficient CNOT gate for spins in silicon will open a path for multi-qubit algorithms in a scalable semiconductor system.Here we demonstrate a ~200 ns CNOT gate in a silicon semiconductor double quantum dot (DQD), nearly an order of magnitude faster than the previously demonstrated composite CNOT gate (9). The gate is implemented by turning on an exchange interaction, which results in a state-selective electron spin resonance (ESR) transition that is used to implement a CNOT gate with a single microwave (MW) pulse. Local magnetic field gradients allow for all-electrical control of the spin states with single qubit gate fidelities exceeding 99%, enabled by the largely nuclear-spin-free environment of the silicon host lattice. In contrast with previous DQD implementations of the exchange gate, our CNOT gate is implemented at a symmetric operating point, where the exchange coupling J is first-order insensitive to charge noise (12,13). By combining the CNOT with single qubit gates we create a Bell state with a fidelity F = 75%, limited primarily by the qubit readout visibility (14). Our demonstration of a universal set of fast quantum gates for spins in silicon paves the way for the first multi-qubit algorithms with semiconductor spin qubits (15).The spin of a single electron is used to encode a qubit (16). A gate-defined DQD (Fig. 1A) is used to isolate two electron...

Entangling gates for electron spins in semiconductor quantum dots are generally based on exchange, a shortranged interaction that requires wavefunction overlap. Coherent spin-photon coupling raises the prospect of using photons as long-distance interconnects for spin qubits. Realizing a key milestone for spin-based quantum information processing, we demonstrate microwave-mediated spin-spin interactions between two electrons that are physically separated by more than 4 mm. Coherent spin-photon coupling is demonstrated for each individual spin using microwave transmission spectroscopy. An enhanced vacuum Rabi splitting is observed when both spins are tuned into resonance with the cavity, indicative of a coherent spin-spin interaction. Our results demonstrate that microwave-frequency photons can be used as a resource to generate long-range two-qubit gates between spatially separated spins.

Strong magnetic field gradients can produce a synthetic spin-orbit interaction that allows for high fidelity electrical control of single electron spins. We investigate how a field gradient impacts the spin relaxation time T1 by measuring T1 as a function of magnetic field B in silicon. The interplay of charge noise, magnetic field gradients, phonons, and conduction band valleys leads to a maximum relaxation time of 160 ms at low field, a strong spin-valley relaxation hotspot at intermediate fields, and a B 4 scaling at high fields. T1 is found to decrease with lattice temperature T lat as well as with added electrical noise. In comparison, samples without micromagnets have a significantly longer T1. Optimization of the micromagnet design, combined with reductions in charge noise and electron temperature, may further extend T1 in devices with large magnetic field gradients.

Motivated by recent experiments of Zajac et al.[1], we theoretically describe high-fidelity twoqubit gates using the exchange interaction between the spins in neighboring quantum dots subject to a magnetic field gradient. We use a combination of analytical calculations and numerical simulations to provide the optimal pulse sequences and parameter settings for the gate operation. We present a novel synchronization method which avoids detrimental spin flips during the gate operation and provide details about phase mismatches accumulated during the two-qubit gates which occur due to residual exchange interaction, non-adiabatic pulses, and off-resonant driving. By adjusting the gate times, synchronizing the resonant and off-resonant transitions, and compensating these phase mismatches by phase control, the overall gate fidelity can be increased significantly.arXiv:1711.00754v1 [cond-mat.mes-hall]

Traditional approaches to controlling single spins in quantum dots require the generation of large electromagnetic fields to drive many Rabi oscillations within the spin coherence time. We demonstrate "flopping-mode" electric dipole spin resonance, where an electron is electrically driven in a Si/SiGe double quantum dot in the presence of a large magnetic field gradient. At zero detuning, charge delocalization across the double quantum dot enhances coupling to the drive field and enables low power electric dipole spin resonance. Through dispersive measurements of the single electron spin state, we demonstrate a nearly three order of magnitude improvement in driving efficiency using flopping-mode resonance, which should facilitate low power spin control in quantum dot arrays.Recent advances in silicon spin qubits have bolstered their standing as a platform for scalable quantum information processing. As single-qubit gate fidelities exceed 99.9% [1], two-qubit gate fidelities improve [2][3][4][5][6], and the field accelerates towards large multi-qubit arrays [7,8], developing the tools necessary for efficient and scalable spin control is critical [9]. While it is possible to implement single electron spin resonance in quantum dots (QDs) using ac magnetic fields [10], the requisite high drive powers and associated heat loads are technically challenging and place limitations on attainable Rabi frequencies [11]. As spin systems are scaled beyond a few qubits, methods of spin control which minimize dissipation and reduce qubit crosstalk will be important for low temperature quantum information processing [12].Electric dipole spin resonance (EDSR) is an alternative to conventional electron spin resonance. In EDSR, static gradient magnetic fields and oscillating electric fields are used to drive spin rotations [13]. The origin of the effective magnetic field gradient varies across implementations: intrinsic spin-orbit coupling [14][15][16], hyperfine coupling [17], and g-factor modulation [18] have been used to couple electric fields to spin states. The inhomogeneous magnetic field generated by a micromagnet [19,20] has been used to create a synthetic spin-orbit field for EDSR, enabling high fidelity control [1]. Conveniently, this magnetic field gradient gives rise to a spatially varying Zeeman splitting, enabling spins in neighboring QDs to be selectively addressed [11,19,[21][22][23][24][25].In this Letter, we demonstrate a novel mechanism for driving low-power, coherent spin rotations, which we call "flopping-mode EDSR". In conventional EDSR, the electric drive field couples to a charge trapped in a single quantum dot, leading to a relatively small electronic displacement [16]. We instead drive single spin rotations in a DQD close to zero detuning, = 0, where the electric field can force the electron to flop back and forth between the left and right dots, thereby sampling a larger variation in transverse magnetic field. We call this configuration the "flopping-mode".Neglecting spin, the Hamiltonian describing a singl...