A challenge for constructing large circuits of superconducting qubits is to balance addressability, coherence and coupling strength. High coherence can be attained by building circuits from fixedfrequency qubits, however, leading techniques cannot couple qubits that are far detuned. Here we introduce a method based on a tunable bus which allows for the coupling of two fixed-frequency qubits even at large detunings. By parametrically oscillating the bus at the qubit-qubit detuning we enable a resonant exchange (XX+YY) interaction. We use this interaction to implement a 183 ns two-qubit iSWAP gate between qubits separated in frequency by 854 MHz with a measured average fidelity of 0.9823(4) from interleaved randomized benchmarking. This gate may be an enabling technology for surface code circuits and for analog quantum simulation.

We experimentally probe the properties of the disordered Bose-Hubbard model using an atomic Bose-Einstein condensate trapped in a 3D disordered optical lattice. Controllable disorder is introduced using a fine-grained optical speckle field with features comparable in size to the lattice spacing along every lattice direction. A precision measurement of the disordering potential is used to compute the single-particle parameters of the system. To constrain theories of the disordered Bose Hubbard model, we have measured the change in condensate fraction as a function of disorder strength for several different ratios of tunneling to interaction energy. We observe disorder-induced, reversible suppression of condensate fraction for superfluid and coexisting superfluid-Mott-insulator phases.

For superconducting qubits, microwave pulses drive rotations around the Bloch sphere. The phase of these drives can be used to generate zero-duration arbitrary "virtual" Z-gates which, combined with two X π/2 gates, can generate any SU(2) gate. Here we show how to best utilize these virtual Z-gates to both improve algorithms and correct pulse errors. We perform randomized benchmarking using a Clifford set of Hadamard and Z-gates and show that the error per Clifford is reduced versus a set consisting of standard finite-duration X and Y gates. Z-gates can correct unitary rotation errors for weakly anharmonic qubits as an alternative to pulse shaping techniques such as DRAG. We investigate leakage and show that a combination of DRAG pulse shaping to minimize leakage and Z-gates to correct rotation errors (DRAGZ) realizes a 13.3 ns X π/2 gate characterized by low error (1.95[3] × 10 −4 ) and low leakage (3.1[6] × 10 −6 ). Ultimately leakage is limited by the finite temperature of the qubit, but this limit is two orders-of-magnitude smaller than pulse errors due to decoherence.Computers based on quantum bits (qubits) are predicted to outperform classical computers for certain critical problems, e.g., factoring. Unlike a classical bit, which is discretely in the state 0 or 1, a qubit can be in a superposition state |Ψ = cos(θ/2)|0 + e iφ sin(θ/2)|1 where |0 and |1 are the quantum versions of the classical 0 and 1 states. This single-qubit superposition state can be geometrically represented as a point on the surface of a unit-sphere known as the Bloch sphere. Critical to implementing a quantum computer is the ability to control the state of the qubit, i.e., transform the qubit state arbitrarily between two points on the Bloch sphere. This is accomplished by unitary transformations (gates), which correspond to rotations of the state around different axes in the Bloch sphere representation. Physically, X and Y gates (rotations around the X and Y axes) are generated by modulating the coupling between the states |0 and |1 at the frequency difference between these states ω 01 = (E |1 −E |0 )/h. This modulation drive has the general form Ω(t) cos(ω D t − γ) where Ω(t) is the drive strength of the rotation, ω D is the drive frequency (ω D = ω 01 on resonance) and γ is the drive phase. The duration of the gate is set by the desired rotation angle and the drive strength. On-resonance, when γ = 0, the qubit state rotates around the X axis and when γ = π 2 the rotation is around the Y axis. Therefore, the geometric X and Y axes in the Bloch sphere correspond to a real π 2 phase difference between drive fields. Rotations around the remaining axis (Z axis), i.e., Zgates, correspond to a change in the relative phase between the |0 and |1 states. A Z-gate can be implemented by either detuning the frequency of the qubit with respect to the drive field for some finite amount of time (e.g. see Ref.[1]) or by composite X and Y gates. The result is that the qubit state rotates with respect to the X and Y axes. However, it is equivalent t...

Optical lattices have emerged as ideal simulators for Hubbard models of strongly correlated materials, such as the high-temperature superconducting cuprates. In optical lattice experiments, microscopic parameters such as the interaction strength between particles are well known and easily tunable. Unfortunately, this benefit of using optical lattices to study Hubbard models comes with one clear disadvantage: the energy scales in atomic systems are typically nanoKelvin compared with Kelvin in solids, with a correspondingly miniscule temperature scale required to observe exotic phases such as d-wave superconductivity. The ultra-low temperatures necessary to reach the regime in which optical lattice simulation can have an impact-the domain in which our theoretical understanding fails-have been a barrier to progress in this field. To move forward, a concerted effort is required to develop new techniques for cooling and, by extension, techniques to measure even lower temperatures. This article will be devoted to discussing the concepts of cooling and thermometry, fundamental sources of heat in optical lattice experiments, and a review of proposed and implemented thermometry and cooling techniques. 4 of the simplest FH model, cool to low temperature, and search for d-wave superfluidity (the analog of SC for neutral atoms). If the simplest FH model is insufficient to generate d-wave SF, then we can add in long-range interactions, disorder, and other features, and determine the impact on the phase diagram. Ultimately, the hope is to use optical lattices to measure the FH phase diagram.Experimental and theoretical work on optical lattice simulation has not been focused solely on the FH model. An in-depth review of proposals can be found in Ref. [9]; here, we mention a few areas that lattices are primed to impact. Bosonic atoms trapped in a lattice realize the Bose-Hubbard (BH) model [26]. In the simplest, spinless BH model, particles tunnel between sites and interact if they are on the same site, just as in the FH model. The primary difference with the FH model are that the particles obey Bose statistics, and therefore particles in the same spin state can interact. While the ground state phase diagram of the BH model is well understood (see , for example), dynamics are not, and lattice experiments are beginning to have an impact on that front [30][31][32][33][34][35][36]. Adding disorder to bosonic particles in an optical lattice is a method for studying the disordered Bose-Hubbard (DBH) model [9,37,38], which has been used as a paradigm for granular superconductors and superfluids in porous media. In the DBH model, the characteristic physical parameters, such as the tunneling energy, vary from site-to-site. Experiments are starting to influence our understanding of the DBH model [39], about which there remain some disputes. Finally, ultra-cold atoms in a lattice can be used to study a variety of interacting spin models that involve magnetic interactions between spins pinned to a lattice (see, for example, Refs. [40][41][...

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We demonstrate fluorescence microscopy of individual fermionic potassium atoms in a 527-nmperiod optical lattice. Using electromagnetically induced transparency (EIT) cooling on the 770.1-nm D1 transition of 40 K, we find that atoms remain at individual sites of a 0.3-mK-deep lattice, with a 1/e pinning lifetime of 67(9) s, while scattering ∼ 10 3 photons per second. The plane to be imaged is isolated using microwave spectroscopy in a magnetic field gradient, and can be chosen at any depth within the three-dimensional lattice. With a similar protocol, we also demonstrate patterned selection within a single lattice plane. High resolution images are acquired using a microscope objective with 0.8 numerical aperture, from which we determine the occupation of lattice sites in the imaging plane with 94(2)% fidelity per atom. Imaging with single-atom sensitivity and addressing with single-site accuracy are key steps towards the search for unconventional superfluidity of fermions in optical lattices, the initialization and characterization of transport and non-equilibrium dynamics, and the observation of magnetic domains.Ultracold fermionic atoms in an optical lattice realize an impurity-free analog of electrons in crystalline materials, with full control of parameters such as interaction strength, dimensionality, and tunneling [1,2]. Furthermore, ultracold systems can study many-body physics in scenarios currently inaccessible to materials, such as gauge fields equivalent to thousands of Tesla [3][4][5], interactions at the unitary limit [6], and quantum manybody physics far from equilibrium [7]. With sufficient control and probes, these experiments can be considered analog quantum simulations [8,9]. However, two important tools have been lacking: imaging and addressing fermionic atoms at the single-site and single-atom level [9]. When applied to bosonic atoms, these tools have already been dramatically successful [10][11][12][13][14][15][16][17][18][19][20].High-resolution imaging and manipulation of ultracold fermions solves several outstanding problems at once. First, in-situ spatial probes directly reveal the order parameter of insulating phases, magnetic domain formation, and other correlations inaccessible in time-of-flight imaging [13,14,19]. Second, an ensemble of density distributions provides a direct measure of entropy [13,14], extending thermometry of lattice fermions [21]. Third, manipulation of atoms with single-site precision can initiate dynamics [15,16], project or remove disorder [14], and selectively remove high entropy atoms to perform in-situ cooling [22,23].This year, five research groups have succeeded in imaging single fermions in an optical lattice: three using Raman sideband cooling [24][25][26] and two using EIT cooling [27], including the results reported in this Article. Our approach is distinguished by a unique imaging configuration, and takes a further step by implementing threedimensional spatial addressing, which is used here for selective removal of atoms from the lattice. Figure 1 ill...

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