When electrons are confined in two dimensions (2D) and subjected to strong magnetic fields, the Coulomb interactions between them become dominant and can lead to novel states of matter such as fractional quantum Hall (FQH) liquids 1 . In these liquids electrons linked to magnetic flux quanta form complex composite quasipartices, which are manifested in the quantization of the Hall conductivity as rational fractions of the conductance quantum. The recent experimental discovery of an anomalous integer quantum Hall effect in graphene has opened up a new avenue in the study of correlated 2D electronic systems, in which the interacting electron wavefunctions are those of massless chiral fermions 2,3 . However, due to the prevailing disorder, graphene has thus far exhibited only weak signatures of correlated electron phenomena 4,5 , despite concerted experimental efforts and intense theoretical interest 6-12 . Here, we report the observation of the fractional quantum Hall effect in ultraclean suspended graphene, supporting the existence of strongly correlated electron states in the presence of a magnetic field. In addition, at low carrier density graphene becomes an insulator with an energy gap tunable by magnetic field. These newly discovered quantum states offer the opportunity to study a new state of matter of strongly correlated Dirac fermions in the presence of large magnetic fields.In a perpendicular magnetic field, the energy spectrum of a clean two-dimensional electron system (2DES) splits into a fan of Landau levels (LLs). When the Fermi energy is tuned to lie between the LLs, the system enters the integer quantum Hall (IQH) regime, in which current is carried by states at the edge of the sample and the overall conductance is quantized as G=νe 2 /h, where ν is an integer Landau level filling factor. Already the first observation of the IQH effect in graphene demonstrated an unusual sequence of filling factors ν=±2,±6,±10..., which differs from previously studied 2DESs. This sequence originates from two peculiar features of graphene: the four-fold spin and pseudo-spin (valley) degeneracy of LLs and the existence of a non-trivial Berry phase associated with the pseudo-spin of Dirac quasiparticles 13 .In clean samples and under very strong magnetic fields, additional IQH states emerge at filling factors ν=0, ±1 4,5 . These fragile IQH states are conjectured to result from electron-electron (e-e) interactions lifting the pseudospin and spin degeneracy of the zeroth LL 14 . The nature of these states, and in particular the unusual ν=0 state, responsible for the divergent resistivity of graphene at high magnetic fields 15 , has raised considerable interest in the effect of e-e interactions among Dirac quasiparticles. In conventional semiconductor heterojunctions such correlation effects are spectacularly manifested in the FQH effect, where new electronic ground states are formed in which the elementary excitations are composite particles with fractional charge 16 . The possibility of a FQH effect in graphene, and t...

Quantum computers have the potential to solve certain interesting problems significantly faster than classical computers. To exploit the power of a quantum computation it is necessary to perform interqubit operations and generate entangled states. Spin qubits are a promising candidate for implementing a quantum processor due to their potential for scalability and miniaturization. However, their weak interactions with the environment, which leads to their long coherence times, makes inter-qubit operations challenging. We perform a controlled two-qubit operation between singlet-triplet qubits using a dynamically decoupled sequence that maintains the two-qubit coupling while decoupling each qubit from its fluctuating environment. Using state tomography we measure the full density matrix of the system and determine the concurrence and the fidelity of the generated state, providing proof of entanglement.Singlet-triplet (S-T 0 ) qubits, a particular realization of spin qubits [1][2][3][4][5][6][7], store quantum information in the joint spin state of two electrons [8][9][10]. The basis states for the S-T 0 qubit can be constructed from the eigenstates of a single electron spin, | ↑〉 and | ↓〉. We choose |S〉 = The qubit can then be described as a two level system with a representation on a Bloch sphere shown in Fig. 1a Universal quantum control is achieved using two physically distinct operations that drive rotations around the x and z-axes of the Bloch sphere [11]. Rotations around the z-axis of the Bloch sphere are driven by the exchange splitting, J , between |S〉 and |T 0 〉, and rotations around the x-axis are driven by a magnetic field gradient, ∆B z between the electrons.We implement the S-T 0 qubit by confining two electrons to a double quantum dot (QD) in a two dimensional electron gas (2DEG) located 91nm below the surface of a GaAs-AlGaAs heterostructure. We deposit local top gates using standard electron beam lithography techniques in order to locally deplete the 2DEG and form the QDs. We operate between the states (0,2) and (1,1) where (n L ,n R ) describes the state with n L (n R ) electrons in the left (right) QD. The |S〉 and |T 0 〉 states, the logical subspace for the qubit, are isolated by applying an external magnetic field of B =700mT in the plane of the device such that the Zeeman splitting makes T + = | ↑↑〉, and T − = | ↓↓〉 energetically inaccessible. The exchange splitting, J , is a function of the difference in energy, , between the levels of the left and right QDs. Pulsed DC electric fields rapidly change , allowing us to switch J on, which drives rotations around the z-axis. When J is off the qubit precesses around the x-axis due to a fixed ∆B z , which is stabilized to ∆B z/2π =30MHz by operating the qubit as a feedback loop between interations of the experiment [12]. Dephasing of the qubit rotations reflects fluctuations in the magnitude of the two control axes, J and ∆B , caused by electrical noise and variation in the magnetic field gradient, respectively. The qubit is rapidly (<50ns) i...

Two level systems that can be reliably controlled and measured hold promise as qubits both for metrology and for quantum information science (QIS). Since a fluctuating environment limits the performance of qubits in both capacities, understanding the environmental coupling and dynamics is key to improving qubit performance. We show measurements of the level splitting and dephasing due to voltage noise of a GaAs singlet-triplet qubit during exchange oscillations. Unexpectedly, the voltage fluctuations are non-Markovian even at high frequencies and exhibit a strong temperature dependence. The magnitude of the fluctuations allows the qubit to be used as a charge sensor with a sensitivity of 2 × 10 −8 e/ √ Hz, two orders of magnitude better than a quantum-limited RF single electron transistor (RF-SET). Based on these measurements we provide recommendations for improving qubit coherence, allowing for higher fidelity operations and improved charge sensitivity. Two level quantum systems (qubits) are emerging as promising candidates both for quantum information processing [1] and for sensitive metrology [2,3]. When prepared in a superposition of two states and allowed to evolve, the state of the system precesses with a frequency proportional to the splitting between the states. However, on a timescale of the coherence time, T 2 , the qubit loses its quantum information due to interactions with its noisy environment. This causes qubit oscillations to decay and limits the fidelity of quantum control and the precision of qubit-based measurements. In this work we study singlet-triplet (S-T 0 ) qubits, a particular realization of spin qubits [4][5][6][7][8][9][10][11], which store quantum information in the joint spin state of two electrons [12][13][14]. We form the qubit in two gate-defined lateral quantum dots (QD) in a GaAs/AlGaAs heterostructure (Fig. 1a). The QDs are depleted until there is exactly one electron left in each, so that the system occupies the so-called (1, 1) charge configuration. Here (n L , n R ) describes a double QD with n L electrons in the left dot and n R electrons in the right dot. This two-electron system has four possible spin states: |S , |T + , |T 0 , and |T − . The |S ,|T 0 subspace is used as the logical subspace for this qubit because it is insensitive to homogeneous magnetic field fluctuations and is manipulable using only pulsed DC electric fields [12,13,15]. The relevant low-lying energy levels of this qubit are shown in Fig. 1c. Two distinct rotations are possible in these devices: rotations around the x-axis of the Bloch sphere driven by difference in magnetic field between the QDs, ∆B z (provided in this experiment by feedback-stabilized hyperfine interactions[16]), and rotations around the z-axis driven by the exchange interaction, J (Fig. 1b) [17]. A |S can be prepared quickly with high fidelity by exchanging an electron with the QD leads, and the projection of the state of the qubit along the z-axis can be measured using RF reflectometery with an adjacent sensing QD (green arrow in ...

Unwanted interaction between a quantum system and its fluctuating environment leads to decoherence and is the primary obstacle to establishing a scalable quantum information processing architecture. Strategies such as environmental and materials engineering, quantum error correction and dynamical decoupling can mitigate decoherence, but generally increase experimental complexity. Here we improve coherence in a qubit using real-time Hamiltonian parameter estimation. Using a rapidly converging Bayesian approach, we precisely measure the splitting in a singlet-triplet spin qubit faster than the surrounding nuclear bath fluctuates. We continuously adjust qubit control parameters based on this information, thereby improving the inhomogenously broadened coherence time from tens of nanoseconds to >2 μs. Because the technique demonstrated here is compatible with arbitrary qubit operations, it is a natural complement to quantum error correction and can be used to improve the performance of a wide variety of qubits in both meteorological and quantum information processing applications.

The central-spin problem is a widely studied model of quantum decoherence. Dynamic nuclear polarization occurs in central-spin systems when electronic angular momentum is transferred to nuclear spins and is exploited in quantum information processing for coherent spin manipulation. However, the mechanisms limiting this process remain only partially understood. Here we show that spin–orbit coupling can quench dynamic nuclear polarization in a GaAs quantum dot, because spin conservation is violated in the electron–nuclear system, despite weak spin–orbit coupling in GaAs. Using Landau–Zener sweeps to measure static and dynamic properties of the electron spin–flip probability, we observe that the size of the spin–orbit and hyperfine interactions depends on the magnitude and direction of applied magnetic field. We find that dynamic nuclear polarization is quenched when the spin–orbit contribution exceeds the hyperfine, in agreement with a theoretical model. Our results shed light on the surprisingly strong effect of spin–orbit coupling in central-spin systems.

We present efficient methods to reliably characterize and tune gate-defined semiconductor spin qubits. Our methods are designed to target the tuning procedures of semiconductor double quantum dot in GaAs heterostructures, but can easily be adapted to other quantum-dot-like qubit systems. These tuning procedures include the characterization of the inter-dot tunnel coupling, the tunnel coupling to the surrounding leads and the identification of the various fast initialization points for the operation of the qubit. Since semiconductor-based spin qubits are compatible with standard semiconductor process technology and hence promise good prospects of scalability, the challenge of efficiently tuning the dot's parameters will only grow in the near future, once the multi-qubit stage is reached. With the anticipation of being used as the basis for future automated tuning protocols, all measurements presented here are fast-to-execute and easy-to-analyze characterization methods. They result in quantitative measures of the relevant qubit parameters within a couple of seconds, and require almost no human interference. arXiv:1801.03755v1 [cond-mat.mes-hall]

We present experimental data and associated theory for correlations in a series of experiments involving repeated Landau-Zener sweeps through the crossing point of a singlet state and a spin aligned triplet state in a GaAs double quantum dot containing two conduction electrons, which are loaded in the singlet state before each sweep, and the final spin is recorded after each sweep. The experiments reported here measure correlations on time scales from 4 µs to 2 ms. When the magnetic field is aligned in a direction such that spin-orbit coupling cannot cause spin flips, the correlation spectrum has prominent peaks centered at zero frequency and at the differences of the Larmor frequencies of the nuclei, on top of a frequency-independent background. When the spin-orbit field is relevant, there are additional peaks, centered at the frequencies of the individual species. A theoretical model which neglects the effects of high-frequency charge noise correctly predicts the positions of the observed peaks, and gives a reasonably accurate prediction of the size of the frequency-independent background, but gives peak areas that are larger than the observed areas by a factor of two or more. The observed peak widths are roughly consistent with predictions based on nuclear dephasing times of the order of 60 µs. However, there is extra weight at the lowest observed frequencies, which suggests the existence of residual correlations on the scale of 2 ms. We speculate on the source of these discrepancies.

No abstract