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...

We report on electron spin resonance (ESR) measurements of phosphorus donors localized in a 200 µm 2 area below the inductive wire of a lumped element superconducting resonator. By combining quantum limited parametric amplification with a low impedance microwave resonator design we are able to detect around 2×10 4 spins with a signal-to-noise ratio (SNR) of 1 in a single shot. The 150 Hz coupling strength between the resonator field and individual spins is significantly larger than the 1 -10 Hz coupling rates obtained with typical coplanar waveguide resonator designs. Due to the larger coupling rate, we find that spin relaxation is dominated by radiative decay into the resonator and dependent upon the spin-resonator detuning, as predicted by Purcell.Electron and nuclear spin magnetic resonance are widely used to characterize a diverse set of paramagnetic materials in biology, chemistry, and physics [1]. They also play an important role in the control and readout of spin qubits as highly coherent carriers of quantum information [2,3]. Improving the sensitivity of spin resonance is an outstanding goal, which has triggered research on a variety of measurement schemes such as optical [4,5], electrical [6][7][8], and mechanical [9] detection.Important progress has also been made by inductively coupling spins to superconducting resonators through the magnetic dipole interaction [10] and by adopting ideas and techniques from circuit quantum electrodynamics [11,12]. Strong collective spin coupling with superconducting resonators and qubits has been demonstrated in various materials such as nitrogen vacancy and P1 centers in diamond [10,13,14], rare earth ions [15], ferromagnets [16], and dopants in silicon [17]. The number of spins involved in most of these experiments is typically 10 10 to 10 13 , far from the single spin limit. In an effort to reduce the number of spins and improve ESR sensitivity, remarkable achievements have recently been made by coupling bismuth donors in silicon to resonators with quality factors exceeding 10 5 [18,19]. In this Letter, we demonstrate a complementary approach to improve ESR sensitivity that is based on the enhancement of the single spin coupling strength to the resonator field by using lumped element resonators [15,18] with reduced characteristic impedance. Increasing the coupling strength is particularly helpful when only moderate quality factors are achievable. This is often the case in the presence of large magnetic fields that are required to achieve spin transitions in the microwave frequency range for the majority of spin species. The measurements presented here are performed in magnetic fields B 0 ≈ 180 mT with phosphorus donors in isotopically purified 28 Si, which are representative of the class of spin systems with a g-factor close to 2. By integrating a Josephson parametric amplifier (JPA) into the detection chain we demonstrate the detection of about 2×104 electron spins with a SNR of 1, which exceeds previously reported sensitivities in phosphorus doped silicon by more...

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]

Silicon spin qubits satisfy the necessary criteria for quantum information processing. However, a demonstration of high-fidelity state preparation and readout combined with high-fidelity single- and two-qubit gates, all of which must be present for quantum error correction, has been lacking. We use a two-qubit Si/SiGe quantum processor to demonstrate state preparation and readout with fidelity greater than 97%, combined with both single- and two-qubit control fidelities exceeding 99%. The operation of the quantum processor is quantitatively characterized using gate set tomography and randomized benchmarking. Our results highlight the potential of silicon spin qubits to become a dominant technology in the development of intermediate-scale quantum processors.

We demonstrate the use of high-Q superconducting coplanar waveguide (CPW) microresonators to perform rapid manipulations on a randomly distributed spin ensemble using very low microwave power (400 nW). This power is compatible with dilution refrigerators, making microwave manipulation of spin ensembles feasible for quantum computing applications. We also describe the use of adiabatic microwave pulses to overcome microwave magnetic field (B 1 ) inhomogeneities inherent to CPW resonators. This allows for uniform control over a randomly distributed spin ensemble. Sensitivity data are reported showing a single shot (no signal averaging) sensitivity to 10 7 spins or 3 × 10 4 spins/ √ Hz with averaging.

Solid state quantum processors based on spins in silicon quantum dots are emerging as a powerful platform for quantum information processing [1][2][3]. High fidelity single-and two-qubit gates have recently been demonstrated [2][3][4][5][6] and large extendable qubit arrays are now routinely fabricated [7,8]. However, two-qubit gates are mediated through nearest-neighbor exchange interactions [1,9], which require direct wavefunction overlap. This limits the overall connectivity of these devices and is a major hurdle to realizing error correction [10], quantum random access memory [11], and multi-qubit quantum algorithms [12]. To extend the connectivity, qubits can be shuttled around a device using quantum SWAP gates, but phase coherent SWAPs have not yet been realized in silicon devices [2][3][4][5][6]. Here, we demonstrate a new single-step resonant SWAP gate. We first use the gate to efficiently initialize and readout our double quantum dot. We then show that the gate can move spin eigenstates in 100 ns with average fidelityF (p) SWAP = 98 %. Finally, the transfer of arbitrary two-qubit product states is benchmarked using state tomography and Clifford randomized benchmarking [5,13], yielding an average fidelity ofF (c) SWAP = 84 % for gate operation times of ∼300 ns. Through coherent spin transport, our resonant SWAP gate enables the coupling of non-adjacent qubits, thus paving the way to large scale experiments using silicon spin qubits.In this work, we use two sites of a quadruple quantum dot fabricated on a 28 Si/SiGe heterostructure [inset of Fig. 1(a)] [8]. Electric dipole spin resonance (EDSR) [14,15] enables single-spin control and an on-chip micromagnet detunes the frequency of each spin to enable site-selective control [8,16]. For demonstration purposes, we use two dots in the device with qubits accumulated under plunger gates P 3 and P 4 . We hereafter refer to the two qubits as Q 3 and Q 4 , respectively. The charge stability diagram of this DQD is shown in Fig. 1(a) and quantum control is performed in the (N i , N i+1 ) = (1, 1) charge configuration, where N i denotes the number of electrons on dot i. We measure the state of Q 4 through spin-selective tunneling to a drain reservoir accumulated beneath gate D 3 [17].There are two modes of operation for the resonant SWAP gate demonstrated in this Letter. First, a projection-SWAP can be used to transfer spin eigenstates Figure 1. (a) Charge stability map for a DQD formed using sites 3 and 4 in the quadruple dot array (inset). Quantum control is performed near the center of the (1,1) charge stability region as denoted by the green circle. Readout of dot 4 is performed at the (1,0)-(1,1) charge transition denoted by the blue triangle. (b) The typical measurement cycle is shown for controlling and reading out two quantum dots. In panel A, the qubits are manipulated and in panel B Q4 is read out through spin-selective tunneling -leaving the qubit in the |↓ state. In panel C, the exchange interaction J34 between Q3 and Q4 is modulated (through modulation of...

Silicon spin qubits are a promising quantum computing platform offering long coherence times, small device sizes, and compatibility with industry-backed device fabrication techniques. In recent years, high fidelity single-qubit and two-qubit operations have been demonstrated in Si. Here, we demonstrate coherent spin control in a quadruple quantum dot fabricated using isotopically enriched 28 Si. We tune the ground state charge configuration of the quadruple dot down to the single electron regime and demonstrate tunable interdot tunnel couplings as large as 20 GHz, which enables exchange-based two-qubit gate operations. Site-selective single spin rotations are achieved using electric dipole spin resonance in a magnetic field gradient. We execute a resonant-CNOT gate between two adjacent spins in 270 ns.Quantum processors based on spins in semiconductors [1-3] are rapidly becoming a strong contender in the global race to build a quantum cofmputer. In particular, silicon is an excellent host material for spin-based quantum computing by virtue of its small spin-orbit coupling and long spin coherence times [4,5]. Within the past few years, tremendous progress has been made in achieving high fidelity single-qubit [6, 7] and two-qubit control [8][9][10][11][12] in silicon. Scalable one-dimensional arrays of silicon quantum dots have been demonstrated [13], and in GaAs, where electron wavefunctions are comparably large, both one-[14-16] and two-dimensional arrays [17,18] of spins have been fabricated. Despite this progress, quantum control of spins in silicon has been limited to one-and two-qubit devices. Scaling beyond two-qubit devices opens the door to important experiments which are currently out of reach, including error correction [19,20], quantum simulation [21][22][23][24], and demonstrations of time crystal phases [25].In this Letter, we demonstrate operation of a fourqubit device fabricated using an isotopically enriched 28 Si/SiGe heterostructure. The device offers independent control of all four qubits, as well as pairwise two-qubit gates mediated by the exchange interaction [26]. We demonstrate control and measurement of the charge state of the array, and operate in the regime where each dot contains only one electron. We perform electric dipole spin resonance (EDSR) spectroscopy on all four qubits to show that they have unique spin resonance frequencies. Finally, we modulate the tunnel coupling between adjacent dots and demonstrate a resonant-CNOT gate [9,27].Four spin qubits are arranged in a linear array using an overlapping gate architecture, as shown in Fig. 1(a) [28]. Single spin qubits are formed by accumulating a electron under each plunger gate: P 1 , P 2 , P 3 , and P 4 . The couplings between dots and between dots and the charge reservoirs formed beneath gates S 3 and D 3 are tuned by adjusting the barrier gate voltages V Bi . Charge sensing is performed by monitoring the currents I S1 and I S2 through two proximal quantum dot charge detectors TS 800 600 650 850 V P4 (mV) 640 700 800 Dot 4 V P1 (m...

The electronic and nuclear spin degrees of freedom of donor impurities in silicon form ultra-coherent two-level systems that are potentially useful for applications in quantum information and are intrinsically compatible with industrial semiconductor processing. However, because of their smaller gyromagnetic ratios, nuclear spins are more difficult to manipulate than electron spins and are often considered too slow for quantum information processing. Moreover, although alternating current magnetic fields are the most natural choice to drive spin transitions and implement quantum gates, they are difficult to confine spatially to the level of a single donor, thus requiring alternative approaches. In recent years, schemes for all-electrical control of donor spin qubits have been proposed but no experimental demonstrations have been reported yet. Here, we demonstrate a scalable all-electric method for controlling neutral P andAs donor nuclear spins in silicon. Using coplanar photonic bandgap resonators, we drive Rabi oscillations on nuclear spins exclusively using electric fields by employing the donor-bound electron as a quantum transducer, much in the spirit of recent works with single-molecule magnets. The electric field confinement leads to major advantages such as low power requirements, higher qubit densities and faster gate times. Additionally, this approach makes it possible to drive nuclear spin qubits either at their resonance frequency or at its first subharmonic, thus reducing device bandwidth requirements. Double quantum transitions can be driven as well, providing easy access to the full computational manifold of our system and making it convenient to implement nuclear spin-based qudits using As donors.