Qubits, the quantum mechanical bits required for quantum computing, must retain their quantum states for times long enough to allow the information contained in them to be processed. In many types of electron-spin qubits, the primary source of information loss is decoherence due to the interaction with nuclear spins of the host lattice. For electrons in gate-defined GaAs quantum dots, spin-echo measurements have revealed coherence times of about 1 µs at magnetic fields below 100 mT (refs 1,2). Here, we show that coherence in such devices can survive much longer, and provide a detailed understanding of the measured nuclearspin-induced decoherence. At fields above a few hundred millitesla, the coherence time measured using a singlepulse spin echo is 30 µs. At lower fields, the echo first collapses, but then revives at times determined by the relative Larmor precession of different nuclear species. This behaviour was recently predicted 3,4 , and can, as we show, be quantitatively accounted for by a semiclassical model for the dynamics of electron and nuclear spins. Using a multiple-pulse Carr-Purcell-Meiboom-Gill echo sequence, the decoherence time can be extended to more than 200 µs, an improvement by two orders of magnitude compared with previous measurements 1,2,5 .The promise of quantum-dot spin qubits as a solid-state approach to quantum computing is demonstrated by the successful realization of initialization, control and single-shot readout of electron-spin qubits in GaAs quantum dots using optical 6 , magnetic 7 and fully electrical 8-10 techniques. To further advance spin-based quantum computing, it is vital to mitigate decoherence due to the interaction of the electron spin with the spins of nuclei of the host material. Understanding the dynamics of this system is also of great fundamental interest 11,12 .Through the hyperfine interaction, an electron spin in a GaAs quantum dot is subjected to an effective magnetic field produced by the nuclear spins. Under typical experimental conditions, this so-called 'Overhauser field' has a random magnitude and direction. Typically, measurements of the coherent electron-spin precession involve averaging over many experimental runs, and thus over many Overhauser field configurations. As a result, the coherence signal is suppressed for evolution times τ ∼ > T 2 * ≈ 10 ns (refs 1, 2). However, the nuclear spins evolve much more slowly than the electron spins, so that the Overhauser field is nearly static over sufficiently short time intervals. Therefore, one can partially eliminate the effect of the random nuclear field by flipping the electron spin halfway through an interval of free precession, a procedure known as Hahn echo. The random contributions of the Overhauser field to the electron-spin precession before and after the spin reversal then approximately cancel out. For longer evolution times, the effective field acting on the electron spin generally changes over the precession interval. This change leads to an eventual loss of coherence on a timescale determined ...

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...

. 2009. Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization. Nature Physics 5(12): 903-908.Published Version

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 ...

Semiconductor spins are one of the few qubit realizations that remain a serious candidate for the implementation of large-scale quantum circuits. Excellent scalability is often argued for spin qubits defined by lithography and controlled via electrical signals, based on the success of conventional semiconductor integrated circuits. However, the wiring and interconnect requirements for quantum circuits are completely different from those for classical circuits, as individual direct current, pulsed and in some cases microwave control signals need to be routed from external sources to every qubit. This is further complicated by the requirement that these spin qubits currently operate at temperatures below 100 mK. Here, we review several strategies that are considered to address this crucial challenge in scaling quantum circuits based on electron spin qubits. Key assets of spin qubits include the potential to operate at 1 to 4 K, the high density of quantum dots or donors combined with possibilities to space them apart as needed, the extremely long-spin coherence times, and the rich options for integration with classical electronics based on the same technology.npj Quantum Information (2017) 3:34 ; doi:10.1038/s41534-017-0038-y INTRODUCTIONThe quantum devices in which quantum bits are stored and processed will form the lowest layer of a complex multi-layer system. 1-3 The system also includes classical electronics to measure and control the qubits, and a conventional computer to control and program these electronics. Increasingly, some of the important challenges involved in these intermediate layers and how they interact have become clear, and there is a strong need for forming a picture of how these challenges can be addressed.Focusing on the interface between the two lowest layers of a quantum computer, each of the quantum bits must receive a long sequence of externally generated control signals that translate to the steps in the computation. Furthermore, given the fragile nature of quantum states, large numbers of quantum bits must be read out periodically to check whether errors occurred along the way, and to correct them. 4 Such error correction is possible provided the probability of error per operation is below the accuracy threshold, which is around 1% for the so-called surface code, a scheme which can be operated on two-dimensional (2D) qubit arrays with nearest-neighbor couplings. 5,6 The read-out data must be processed rapidly and fed back to the qubits in the form of control signals. Since each qubit must separately interface with the outside world, the classical control system must scale along with the number of qubits, and so must the interface between qubits and classical control.The estimated number of physical qubits required for solving relevant problems in quantum chemistry or code breaking is in the 10 6 -10 8 range, using currently known quantum algorithms and quantum error correction methods. 7,8 For comparison, state-

In many realizations of electron spin qubits the dominant source of decoherence is the fluctuating nuclear spin bath of the host material. The slowness of this bath lends itself to a promising mitigation strategy where the nuclear spin bath is prepared in a narrowed state with suppressed fluctuations. Here, this approach is realized for a two-electron spin qubit in a GaAs double quantum dot and a nearly ten-fold increase in the inhomogeneous dephasing time T * 2 is demonstrated. Between subsequent measurements, the bath is prepared by using the qubit as a feedback loop that first measures its nuclear environment by coherent precession, and then polarizes it depending on the final state. This procedure results in a stable fixed point at a nonzero polarization gradient between the two dots, which enables fast universal qubit control.PACS numbers: 73.21. La, 03.67.Lx, 76.70.Fz Spins in semiconductors are attractive qubits because of their long coherence times [1][2][3], their electrical control and readout [4], and their potential for scalability [5]. Few-electron quantum dot devices have been used successfully in recent years to demonstrate universal control of electron spin qubits as well as single shot readout [6][7][8][9]. However, interaction of the qubit spin(s) with nearby nuclear spins is a significant source of decoherence in several systems [2-4, 10, 11]. It is therefore very attractive to prepare the spin environment of the electron in a way that mitigates this decoherence. One approach would be to polarize it [12], but the nearly complete polarization required for improved coherence[13] is difficult to achieve.Here, we present a method to narrow the distribution of the fluctuating nuclear hyperfine field while maintaining a weak polarization. In addition to the reduced decoherence, such a narrowed state is of interest for studying the long-time quantum dynamics arising from the spinbath interaction [14]. Our method relies on first letting the qubit evolve under the influence of the bath. The resulting final state of the qubit controls the effectiveness of a subsequent dynamic nuclear polarization step. The qubit thus acts as a complete feedback loop, and the outcome of its measurement of the controlled variable does not need to be known to the outside world.Electron-nuclear feedback mechanisms were previously observed in resonance locking experiments under microwave [15] and optical irradiation [16][17][18]. In Refs. [15,17], a narrowing of the hyperfine field was inferred from the observed bidirectional polarization keeping the system on resonance, but not experimentally verified. In Ref.[16], narrowing was detected spectroscopically, and Ref.[18] studied an ensemble of optically controlled quantum dots. Here, we directly measure the narrowed distribution of the hyperfine field and the dephasing time, T * 2 , of a single, electrically controlled qubit. T * 2 is enhanced by nearly an order of magnitude. In contrast to previous experiments, where the feedback mechanism is intrinsic to the polarization...

Quantum mechanics predicts that the equilibrium state of a resistive electrical circuit contains a dissipationless current. This persistent current has been the focus of considerable theoretical and experimental work, but its basic properties remain a topic of controversy. The main experimental challenges in studying persistent currents have been the small signals they produce and their exceptional sensitivity to their environment. To address these issues we have developed a new technique for detecting persistent currents which offers greatly improved sensitivity and reduced measurement back action. This allows us to measure the persistent current in metal rings over a wider range of temperature, ring size, and magnetic field than has been possible previously. We find that measurements of both a single ring and arrays of rings agree well with calculations based on a model of non-interacting electrons. An electrical current induced in a resistive circuit will rapidly decay in the absence of an applied voltage. This decay reflects the tendency of the circuit's electrons to dissipate energy and relax to their ground state. However quantum mechanics predicts that the electrons' many-body ground state (and, at finite temperature, their thermal equilibrium state) may itself contain a "persistent" current which flows through the resistive circuit without dissipating energy or decaying. A dissipationless equilibrium current flowing through a resistive circuit is highly counterintuitive, but it has a familiar analog in atomic physics: some atomic species' electronic ground states possess non-zero orbital angular momentum, equivalent to a current circulating around the atom. Theoretical treatments of persistent currents (PC) in resistive metal rings have been developed over a number of decades (see [1,2] and references therein). Calculations which take 1

Fluctuations are important near phase transitions, where they can be difficult to describe quantitatively. Superconductivity in mesoscopic rings is particularly intriguing because the critical temperature is an oscillatory function of magnetic field. There is an exact theory for thermal fluctuations in one-dimensional superconducting rings, which are therefore expected to be an excellent model system. We measured the susceptibility of many rings, one ring at a time, by using a scanning superconducting quantum interference device that can isolate magnetic signals that are seven orders of magnitude smaller than applied flux. We find that the fluctuation theory describes the results and that a single parameter characterizes the ways in which the fluctuations are especially important at magnetic fields where the critical temperature is suppressed.