We propose a quantum dot qubit architecture that has an attractive combination of speed and fabrication simplicity. It consists of a double quantum dot with one electron in one dot and two electrons in the other. The qubit itself is a set of two states with total spin quantum numbers S(2)=3/4 (S=1/2) and S(z)=-1/2, with the two different states being singlet and triplet in the doubly occupied dot. Gate operations can be implemented electrically and the qubit is highly tunable, enabling fast implementation of one- and two-qubit gates in a simpler geometry and with fewer operations than in other proposed quantum dot qubit architectures with fast operations. Moreover, the system has potentially long decoherence times. These are all extremely attractive properties for use in quantum information processing devices.

The similarities between gated quantum dots and the transistors in modern microelectronics--in fabrication methods, physical structure and voltage scales for manipulation--have led to great interest in the development of quantum bits (qubits) in semiconductor quantum dots. Although quantum dot spin qubits have demonstrated long coherence times, their manipulation is often slower than desired for important future applications, such as factoring. Furthermore, scalability and manufacturability are enhanced when qubits are as simple as possible. Previous work has increased the speed of spin qubit rotations by making use of integrated micromagnets, dynamic pumping of nuclear spins or the addition of a third quantum dot. Here we demonstrate a qubit that is a hybrid of spin and charge. It is simple, requiring neither nuclear-state preparation nor micromagnets. Unlike previous double-dot qubits, the hybrid qubit enables fast rotations about two axes of the Bloch sphere. We demonstrate full control on the Bloch sphere with π-rotation times of less than 100 picoseconds in two orthogonal directions, which is more than an order of magnitude faster than any other double-dot qubit. The speed arises from the qubit's charge-like characteristics, and its spin-like features result in resistance to decoherence over a wide range of gate voltages. We achieve full process tomography in our electrically controlled semiconductor quantum dot qubit, extracting high fidelities of 85 per cent for X rotations (transitions between qubit states) and 94 per cent for Z rotations (phase accumulation between qubit states).

The remarkable properties of silicon have made it the central material for the fabrication of current microelectronic devices. Silicon's fundamental properties also make it an attractive option for the development of devices for spintronics [1] and quantum information processing [2][3][4][5]. The ability to manipulate and measure spins of single electrons is crucial for these applications. Here we report the manipulation and measurement of a single spin in a quantum dot fabricated in a silicon/silicon-germanium heterostructure. We demonstrate that the rate of loading of electrons into the device can be tuned over an order of magnitude using a gate voltage, that the spin state of the loaded electron depends systematically on the loading voltage level, and that this tunability arises because electron spins can be loaded through excited orbital states of the quantum dot. The longitudinal spin relaxation time T 1 is measured using single-shot pulsed techniques [6] and found to be ∼ 3 seconds at a field of 1.85 Tesla. The demonstration of single spin measurement as well as a long spin relaxation time and tunability of the loading are all favorable properties for spintronics and quantum information processing applications.Silicon is a material in which spin qubits are expected to have long coherence times, thanks to the predominance of a spin-zero nuclear isotope and relatively weak spin-orbit coupling. However, silicon quantum dots have yet to demonstrate the reproducibility and controllability achieved in gallium arsenide devices [7][8][9][10]. Here, we demonstrate the control and manipulation of spin states of single electrons in a silicon/silicon-germanium (Si/SiGe) quantum dot and report the first single-shot measurements of the longitudinal spin relaxation time T 1 in such devices. We also show that the presence of a relatively low-lying spin-split orbital excited state in the dot can be exploited to increase the speed and tunability of the loading of spins into the dot. Our results demonstrate that Si/SiGe quantum dots can be fabricated that are sufficiently tunable to enable single-electron manipulation and measurement, and that long spin relaxation times are consistent with the orbital and/or valley excitation energies in these systems.The measurements we report were performed on a gate-defined quantum dot with the gate configuration shown in Fig. 1a, tuned to be in the single-dot regime. The dot is measured at low temperature and in a parallel magnetic field. As shown in Fig. 1b, an electron can be loaded into one of four energy eigenstates; we denote the states, in order of increasing energy, as | ↓ g , | ↑ g , | ↓ e , and | ↑ e , where the first index refers to spin (↓ having lower energy than ↑ ) and the second to the ground (g) and excited (e) orbital levels. We obtain an experimental map of these states by measuring the differential current dI QPC /dV L through a charge sensing quantum point contact while applying square voltage pulses to gate L. The grayscale plots of dI QPC /dV L in Fig. 1c,d arXiv:10...

A quantum dot hybrid qubit formed from three electrons in a double quantum dot has the potential for great speed, due to presence of level crossings where the qubit becomes charge-like. Here, we show how to take full advantage of the level crossings in a pulsed gating scheme, which decomposes the spin qubit into a series of charge transitions. We develop one and two-qubit dc quantum gates that are simpler than the previously proposed ac gates. We obtain closed form solutions for the control sequences and show that these sub-nanosecond gates can achieve high fidelities.PACS numbers: 03.67. Lx,73.21.La,85.35.Be A key figure of merit for a quantum information processing device is the ratio of the quantum coherence time to the time required to perform qubit gate manipulations [1][2][3]. The recently proposed hybrid quantum dot qubit [4] is a relatively simple qubit architecture that could achieve a higher figure of merit than previous qubit designs [5][6][7]. The qubit itself is a set of two states with total spin quantum numbers S 2 = 3/4 (S = 1 2 ) and S z = − 1 2 , with the two different states using the singlet and triplet in a doubly-occupied dot and a single spin in a singly-occupied dot. The two states of the qubit have different energies, and Ref. 4 proposes to implement gate operations using high-frequency (∼10−40 GHz) resonant RF pulses. This method is feasible [8,9], but it is significantly more complicated to implement experimentally than the pulse-gating methods used for charge qubits in Refs. 10-14 and for spin qubits in Refs. 15-19. Here we show how to implement pulse-gating of the quantum dot hybrid qubit. One-and two-qubit gates require a modest number of non-adiabatic voltage pulses (five and eight, respectively), each of which is similar to those already used for gate operations on charge qubits and singlettriplet spin quits.The two logical qubit states of the hybrid quantum dot qubit are |0 L = |S |↓ and |1 L = 1 3 |T 0 |↓ − 2 3 |T − |↑ , where |S , |T − , and |T 0 are two-particle singlet (S) and triplet (T) states in the left dot, and |↑ and |↓ respectively denote a spin-up and spin-down electron in the right dot. These states form a decoherencefree subspace that is insensitive to long-wavelength magnetic flux noise; moreover, decoherence processes that do not explicitly couple to spin or induce a transition of an electron to the reservoir do not induce transitions that go outside of the subspace of an individual qubit [20]. The qubit has the same symmetries in spin space as the tripledot qubit proposed by DiVincenzo et al. [7], but is simpler to fabricate because it requires a double dot instead of a triple dot. Transitions between the logical qubit states |0 L and |1 L are allowed when tunneling is introduced between the dots. The physical process that leads to transitions between the two logical qubit states |0 L and |1 L involves an intermediate state |E that has one electron in the left dot and two electrons in the right dot, and the same total S 2 and S z . Fig. 1(a) is a schematic of ...

An important goal in the manipulation of quantum systems is the achievement of many coherent oscillations within the characteristic dephasing time T Ã 2 . Most manipulations of electron spins in quantum dots have focused on the construction and control of two-state quantum systems, or qubits, in which each quantum dot is occupied by a single electron. Here we perform quantum manipulations on a system with three electrons per double quantum dot. We demonstrate that tailored pulse sequences can be used to induce coherent rotations between three-electron quantum states. Certain pulse sequences yield coherent oscillations fast enough that more than 100 oscillations are visible within a T Ã 2 time. The minimum oscillation frequency we observe is faster than 5 GHz. The presence of the third electron enables very fast rotations to all possible states, in contrast to the case when only two electrons are used, in which some rotations are slow.

Fast quantum oscillations of a charge qubit in a double quantum dot fabricated in a Si/SiGe heterostructure are demonstrated and characterized experimentally. The measured inhomogeneous dephasing time T * 2 ranges from 127 ps to 2.1 ns; it depends substantially on how the energy difference of the two qubit states varies with external voltages, consistent with a decoherence process that is dominated by detuning noise (charge noise that changes the asymmetry of the qubit's double-well potential). In the regime with the shortest T * 2 , applying a charge-echo pulse sequence increases the measured inhomogeneous decoherence time from 127 to 760 ps, demonstrating that low-frequency noise processes are an important dephasing mechanism.

Several logical qubits and quantum gates have been proposed for semiconductor quantum dots controlled by voltages applied to top gates. The different schemes can be difficult to compare meaningfully. Here we develop a theoretical framework to evaluate disparate qubit-gating schemes on an equal footing. We apply the procedure to two types of double-dot qubits: the singlet-triplet and the semiconducting quantum dot hybrid qubit. We investigate three quantum gates that flip the qubit state: a DC pulsed gate, an AC gate based on logical qubit resonance, and a gate-like process known as stimulated Raman adiabatic passage. These gates are all mediated by an exchange interaction that is controlled experimentally using the interdot tunnel coupling g and the detuning e, which sets the energy difference between the dots. Our procedure has two steps. First, we optimize the gate fidelity (f) for fixed g as a function of the other control parameters; this yields an f opt (g) that is universal for different types of gates. Next, we identify physical constraints on the control parameters; this yields an upper bound f max that is specific to the qubit-gate combination. We show that similar gate fidelities (∼ 99:5%) should be attainable for singlet-triplet qubits in isotopically purified Si, and for hybrid qubits in natural Si. Considerably lower fidelities are obtained for GaAs devices, due to the fluctuating magnetic fields ΔB produced by nuclear spins.quantum computing | Heisenberg exchange | decoherence T he fundamental building block of a quantum information processor is a two-state quantum system, or qubit. Solid-state qubits based on electrons confined in top-gated quantum dots in semiconductor heterostructures (1) are promising, due to the promise of manipulability and the overall maturity of semiconductor technology. In a charge qubit, the information is stored in the location of an electron in a double quantum dot. Because charge qubits are subject to strong Coulomb interactions, they can be manipulated quickly, at gigahertz frequencies, using control electronics (2-5); however, they also couple strongly to environmental noise sources, such as thermally activated charges on materials defects, leading to short, subnanosecond decoherence times (6). Spin qubits, which couple more weakly to environmental noise, have much longer coherence times (1, 7-15). However, because magnetic couplings are weak, gate operations between spin qubits are slow. For this reason, in most gating protocols, spin qubits adopt a charge character briefly during gate operations. Successful gate operations generally entail a tradeoff: charge-like for faster gates vs. spin-like for better coherence.Several types of logical qubits have been designed to enable electrically controlled manipulation and measurement of qubits encoded in spin degrees of freedom formed of two or more electrons in two (7, 9, 16) or three (11) coupled dots. These logical qubits share experimental control knobs; however, their spin-charge characteristics vary widely, yielding ...

Optimal working points or "sweet spots" have arisen as an important tool for mitigating charge noise in quantum dot logical spin qubits. The exchange-only qubit provides an ideal system for studying this effect because Z rotations are performed directly at the sweet spot, while X rotations are not. Here for the first time we quantify the ability of the sweet spot to mitigate charge noise by treating X and Z rotations on an equal footing. Specifically, we optimize X rotations and determine an upper bound on their fidelity. We find that sweet spots offer a fidelity improvement factor of at least 20 for typical GaAs devices, and more for Si devices.