We introduce a superconducting qubit architecture that combines high-coherence qubits and tunable qubit-qubit coupling. With the ability to set the coupling to zero, we demonstrate that this architecture is protected from the frequency crowding problems that arise from fixed coupling. More importantly, the coupling can be tuned dynamically with nanosecond resolution, making this architecture a versatile platform with applications ranging from quantum logic gates to quantum simulation. We illustrate the advantages of dynamic coupling by implementing a novel adiabatic controlled-Z gate, at a speed approaching that of single-qubit gates. Integrating coherence and scalable control, our "gmon" architecture is a promising path towards large-scale quantum computation and simulation.The fundamental challenge for quantum computation and simulation is to construct a large-scale network of highly connected coherent qubits [1, 2]. Superconducting qubits use macroscopic circuits to process quantum information and are a promising candidate towards this end [3]. Over the last several years, materials research and circuit optimization have led to significant progress in qubit coherence [4][5][6]. Superconducting qubits can now perform hundreds of operations within their coherence times, allowing for research into complex algorithms such as error correction [7,8].It is desirable to combine these high-coherence qubits with tunable inter-qubit coupling; the resulting architecture would allow for both coherent local operations and dynamically varying qubit interactions. For quantum simulation, this would provide a unique opportunity to investigate dynamic processes in non-equilibrium condensed matter phenomena [9][10][11][12][13]. For quantum computation, such an architecture would provide isolation for single-qubit gates while at the same time enabling fast two-qubit gates that minimize errors from decoherence. Despite previous successful demonstrations of tunable coupling [14][15][16][17][18][19][20][21][22][23], these applications have yet to be realized due to the challenge of incorporating tunable coupling with high coherence devices.Here, we introduce a planar qubit architecture that combines high coherence with tunable inter-qubit coupling g. This "gmon" device is based on the Xmon transmon design [5], but now gives nanosecond control of the coupling strength with a measured on/off coupling ratio exceeding 1000. We find that our device retains the high coherence inherent in the Xmon design, with the coupler providing unique advantages in constructing single-and two-qubit quantum logic gates. With the coupling turned off, we demonstrate that our architecture is protected from the frequency crowding problems that arise from fixed coupling. Our single-qubit gate fidelity is nearly independent of the qubit-qubit detuning, even when operating the qubits on resonance. By dynamically tuning the coupling, we implement a novel adiabatic controlled-Z gate at a speed approaching that of single-qubit gates.A two-qubit unit cell with tun...

We propose a quantum computing architecture based on the integration of nanomechanical resonators with Josephson-junction phase qubits. The resonators are GHz-frequency, dilatational disk resonators, which couple to the junctions through a piezoelectric interaction. The system is analogous to a collection of tunable few-level atoms (the Josephson junctions) coupled to one or more electromagnetic cavities (the resonators). Our architecture combines desirable features of solid-state and optical approaches and may make quantum computing possible in a scalable, solid-state environment.

In quantum information processing, qudits (d-level systems) are an extension of qubits that could speed up certain computing tasks. We demonstrate the operation of a superconducting phase qudit with a number of levels d up to d = 5 and show how to manipulate and measure the qudit state, including simultaneous control of multiple transitions. We used the qudit to emulate the dynamics of single spins with principal quantum number s = 1/2, 1, and 3/2, allowing a measurement of Berry's phase and the even parity of integer spins (and odd parity of half-integer spins) under 2pi-rotation. This extension of the two-level qubit to a multilevel qudit holds promise for more-complex quantum computational architectures and for richer simulations of quantum mechanical systems.

A controlled-phase gate was demonstrated in superconducting Xmon transmon qubits with fidelity reaching 99.4%, relying on the adiabatic interaction between the |11 and |02 states. Here we explain the theoretical concepts behind this protocol that achieves fast gate times with only σz control of the Hamiltonian, based on a theory of non-linear mapping of state errors to a power spectral density and use of optimal window functions. With a solution given in the Fourier basis, optimization is shown to be straightforward for practical cases of an arbitrary state change and finite bandwidth of control signals. We find that errors below 10 −4 are readily achievable for realistic control waveforms.

We construct the effective Hamiltonian describing the motion of electrons in compositionally graded crystals which is valid throughout a given energy band and part way into the gaps. Near the edges of a simple or degenerate band this effective Hamiltonian reduces to an effective mass Hamiltonian with position dependent effective mass. Next, we examine more general states-not restricted to the vicinity of a band edge-in crystals with composition and applied potential variation in one direction. We obtain a WKB-type solution for the envelope functions, as well as the appropriate turning point connection rules.PACS numbers: 73.20. Dx, 71.50.+t, In recent years, the ability to fabricate semiconductor nanostructures with highly controlled variable chemical composition has led to a renewed interest in the physics of electrons in nearly periodic fields and at interfaces. In this Letter we present some results of an ongoing investigation into this subject: (i) First, an effective Hamiltonian 7i is constructed that describes the behavior of electrons in a semiconductor whose composition has a slow spatial variation-slow enough so the concept of a local "band" is well defined. This will be the case when the length scale over which the composition varies is much larger than a lattice constant. The accuracy of this effective Hamiltonian depends only on the composition gradient-// is valid throughout a given energy band and part way into the gaps, (ii) Second, we use this effective Hamiltonian to (a) derive effective mass Hamiltonians valid near the edges of simple and degenerate bands (settling a controversy in the literature [1-11]), and (b) derive a WKB-type envelope function and associated turning point connection rules for states, not necessarily near a band edge, in crystals with composition and applied potential variation in one direction.Consider first a random alloy A C B\-C with a spatially uniform composition characterized by c. Any particular sample, 7, will have a nonperiodic single-particle potential Vj(r,c) due to the particular positions of the type A and B atoms. We now define a periodic potential, V(r,c) = (K/(r,c)>, where () represents the ensemble average over all atomic configurations having a fraction c of type A atoms. This approximation is similar to the virtual crystal approximation [12], a linear interpolation between K(r,0) and K(r, 1). We assume the knowledge of the band structures E n (k,c) associated with the periodic potentials V(r,c). Next consider a sample with a composition c(r) varying slowly on the scale of a lattice constant. We shall call V(r,c(r)) the nearly periodic potential and £"(k,c(r)) the local band structure of the alloy.For simplicity, we consider a monatomic Bravais lattice /=XJ = i/«b a , where the b a are the three smallest primitive lattice vectors. We assume that the primitive lattice vectors b a are independent of c. Most of the results we will present are valid for arbitrary crystal structures-the places where the Bravais lattice assumption is explicitly used will be note...