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Based on a quantum analysis of two capacitively coupled current-biased Josephson junctions, we propose two fundamental two-qubit quantum logic gates. Each of these gates, when supplemented by single-qubit operations, is sufficient for universal quantum computation. Numerical solutions of the time-dependent Schrödinger equation demonstrate that these operations can be performed with good fidelity. The current-biased Josephson junction is an easily fabricated device with great promise as a scalable solid-state qubit [1], as demonstrated by the recent observations of Rabi oscillations [2,3]. This phase qubit is controlled through manipulation of the bias currents and application of microwave pulses resonant with the energy level splitting [2].In this Letter we analyze the quantum dynamics of two coupled phase qubits. (The classical dynamics of this system has also been studied recently [4]). We identify two quantum logic gates that, together with single-qubit operations, provide all necessary ingredients for a universal quantum computer. We perform full dynamical simulations of these gates through numerical integration of the time-dependent Schrödinger equation. These two-qubit operations may be experimentally probed with the methods already used to observe single junction Rabi oscillations [2,3]. Such experiments are of fundamental importance: the successful demonstration of macroscopic quantum entanglement holds profound implications for the universal validity of quantum mechanics [5]. Important progress toward this goal are the temporal oscillations of coupled charge qubits [6] and spectroscopic measurements [7] on the system considered here. Finally, our methods are applicable to the other promising superconducting proposals based on charge, flux, and hybrid realizations [8].Figure 1(a) shows the circuit diagram of our coupled qubits. Each junction has characteristic capacitance C J and critical current I c , and they are coupled by capacitance C C . The two degrees of freedom of this system are the phase differences γ 1 and γ 2 , with dynamics governed by the Hamiltonian [9]Here we have employed the charging and Josephson energies E C = e 2 /2C J and E J = I c /2e, the normalized bias currents J 1 = I 1 /I c , J 2 = I 2 /I c , and the dimensionless coupling parameter ζ = C C /(C C + C J ). This coupling scheme has been recently analyzed [9, 10, 11] and results in a system with easily tuned energy levels and adjustable effective coupling. While ζ is typically fixed by fabrication, the energy levels and the effective coupling of the associated eigenstates are under experimental control through J 1 and J 2 . As shown below, the two junctions are decoupled for J 1 and J 2 sufficiently different, but if J 1 and J 2 are related in certain ways, the junctions are maximally coupled. To illustrate this method of control, we define a reference bias current J 0 and consider the variation of J 1 and J 2 through a detuning parameter ǫ:Quantum logic gates are implemented by varying ǫ with time as shown in Fig. 1(b). This ra...

We present spectroscopic evidence for the creation of entangled macroscopic quantum states in two current-biased Josephson-junction qubits coupled by a capacitor. The individual junction bias currents are used to control the interaction between the qubits by tuning the energy level spacings of the junctions in and out of resonance with each other. Microwave spectroscopy in the 4 to 6 gigahertzrange at 20 millikelvin reveals energy levels that agree well with theoretical results for entangled states. The single qubits are spatially separate, and the entangled states extend over the 0.7-millimeter distance between the two qubits.

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