Philip R. Johnson

Quantum logic gates for coupled superconducting phase qubits

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.

Stochastic Theory of Relativistic Particles Moving in a Quantum Field: II. Scalar Abraham-Lorentz-Dirac-Langevin Equation, Radiation Reaction and Vacuum Fluctuations

We apply the open systems concept and the influence functional formalism introduced in Paper I to establish a stochastic theory of relativistic moving spinless particles in a quantum scalar field. The stochastic regime resting between the quantum and semi-classical captures the statistical mechanical attributes of the full theory. Applying the particlecentric world-line quantization formulation to the quantum field theory of scalar QED we derive a time-dependent (scalar) Abraham-Lorentz-Dirac (ALD) equation and show that it is the correct semiclassical limit for nonlinear particle-field systems without the need of making the dipole or non-relativistic approximations. Progressing to the stochastic regime, we derive multiparticle time-dependent ALD-Langevin equations for nonlinearly coupled particle-field systems. With these equations we show how to address time-dependent dissipation/noise/renormalization in the semiclassical and stochastic limits of QED. We clarify the relation of radiation reaction, quantum dissipation and vacuum fluctuations and the role that initial conditions may play in producing non-Lorentz invariant noise. We emphasize the fundamental role of decoherence in reaching the semiclassical limit, which also suggests the correct way to think about the issues of runaway solutions and preacceleration from the presence of third derivative terms in the ALD equation. We show that the semiclassical self-consistent solutions obtained in this way are “paradox” and pathology free both technically and conceptually. This self-consistent treatment serves as a new platform for investigations into problems related to relativistic moving charges.

Spectroscopy of three-particle entanglement in a macroscopic superconducting circuit.

We study the quantum mechanical behavior of a macroscopic, three-body, superconducting circuit. Microwave spectroscopy on our system, a resonator coupling two large Josephson junctions, produced complex energy spectra well explained by quantum theory over a large frequency range. By tuning each junction separately into resonance with the resonator, we first observe strong coupling between each junction and the resonator. Bringing both junctions together into resonance with the resonator, we find spectroscopic evidence for entanglement between all 3 degrees of freedom and suggest a new method for controllable coupling of distant qubits, a key step toward quantum computation.

Uniformly Accelerated Charge in a Quantum Field: From Radiation Reaction to Unruh Effect

We present a stochastic theory for the nonequilibriurn dynamics of charges moving in a quantum scalar field based on the worldline influence functional and the close-time-path (CTP or in-in) coarse-grained effective action method. We summarize (1) the steps leading to a derivation of a modified Abraham-Lorentz-Dirac equation whose solutions describe a causal semiclassical theory free of runaway solutions and without pre-acceleration patholigies, and (2) the transformation to a stochastic effective action, which generates Abraham-Lorentz-Dirac-Langevin equations depicting the fluctuations of a particle’s worldline around its semiclassical trajectory. We point out the misconceptions in trying to directly relate radiation reaction to vacuum fluctuations, and discuss how, in the framework that we have developed, an array of phenomena, from classical radiation and radiation reaction to the Unruh effect, are interrelated to each other as manifestations at the classical, stochastic and quantum levels. Using this method we give a derivation of the Unruh effect for the spacetime worldline coordinates of an accelerating charge. Our stochastic particle-field model, which was inspired by earlier work in cosmological backreaction, can be used as an analog to the black hole backreaction problem describing the stochastic dynamics of a black hole event horizon.

Spectroscopy of capacitively coupled Josephson-junction qubits

We show that two capacitively coupled Josephson junctions, in the quantum limit, form a simple coupled qubit system with effective coupling controlled by the junction bias currents. We compute numerically the energy levels and wave functions for the system, and show how these may be tuned to make optimal qubits. The dependence of the energy levels on the parameters can be measured spectroscopically, providing an important experimental test for the presence of entangled multiqubit states in Josephson-junction based circuits.

Macroscopic Tunnel Splittings in Superconducting Phase Qubits

Prototype Josephson-junction based qubit coherence times are too short for quantum computing. Recent experiments probing superconducting phase qubits have revealed previously unseen fine splittings in the transition energy spectra. These splittings have been attributed to new microscopic degrees of freedom (microresonators), a previously unknown source of decoherence. We show that macroscopic resonant tunneling in the extremely asymmetric double-well potential of the phase qubit can have observational consequences that are strikingly similar to the observed data.

Capacitively coupled Josephson junctions: A two-qubit system

We describe how single Josephson junctions can be connected together capacitively to form a two-qubit system. We discuss the general behavior of this system show the energy level dependence on various junction parameters and choice of coupling strengths. We also discuss measurement techniques for reading out both qubits which are relevant to our ongoing experiments.

Cooper-pair box as a variable capacitor

We calculate the effective capacitance of a Cooper-pair box and demonstrate that the Cooper-pair box can be used as a variable capacitor. The gate voltage modulates the charge transfer through the small junction in the Cooper-pair box, leading to a gate-dependent capacitance. We describe ongoing experiments to use an Al/AlO/sub x//Al Cooper-pair box as a tunable circuit element at milli-Kelvin temperatures and discuss possible applications to quantum computing as a variable coupling element between two Josephson junction qubits.

The propagation of quantum relativistic wavepackets in electromagnetic fields

We describe the simulation of a quantum relativistic wavepacket propagating in electric and magnetic fields. We start from first principles in QED with the intent of exploring the effects of spin, extended wavepackets, and radiation reaction on particle motion. (This initial work neglects radiation reaction and anti-particle effects). In the numerical simulation of wavepackets we use unitary integrators, adapted to particle propagation in a background (though possibly time-dependent) vector potential.

Quantum control of superconducting phase qubits

We describe quantum control for implementing fast universal quantum gates using Josephson junction-based phase qubits. We have determined the effects of quantum tunneling and leakage on the gate fidelity by performing nonperturbative simulations of the Schrodinger equation. Phase qubits are seen to have many attractive features, and an experimental demonstration of a simple phase-qubit quantum gate should be possible in the near future.