Coupled Flux Qubits Research Articles

Consistency of Ground State and Spectroscopic Measurements on Flux Qubits

We compare the results of ground state and spectroscopic measurements carried out on superconducting flux qubits which are effective two-level quantum systems. For a single qubit and for two coupled qubits we show excellent agreement between the parameters of the pseudospin Hamiltonian found using both methods. We argue that by making use of the ground state measurements the Hamiltonian of N coupled flux qubits can be reconstructed as well at temperatures smaller than the energy level separation. Such a reconstruction of a many-qubit Hamiltonian can be useful for future quantum information processing devices.

Diffusion and transfer of entanglement in an array of inductively coupled flux qubits

A theoretical scheme to generate multipartite entangled states in a Josephson planar-designed architecture is reported. This scheme improves the one published by Migliore et al. [Phys. Rev. B 74, 104503 (2006)] since it speeds up the generation of $W$ entangled states in an $M\ifmmode\times\else\texttimes\fi{}N$ array of inductively coupled Josephson flux qubits by reducing the number of necessary steps. In addition, the same protocol is shown to be able to transfer the $W$ state from one row to the other.

Demonstration of controlled-NOT quantum gates on a pair of superconducting quantum bits

Quantum computation requires quantum logic gates that use the interaction within pairs of quantum bits (qubits) to perform conditional operations. Superconducting qubits may offer an attractive route towards scalable quantum computing. In previous experiments on coupled superconducting qubits, conditional gate behaviour and entanglement were demonstrated. Here we demonstrate selective execution of the complete set of four different controlled-NOT (CNOT) quantum logic gates, by applying microwave pulses of appropriate frequency to a single pair of coupled flux qubits. All two-qubit computational basis states and their superpositions are used as input, while two independent single-shot SQUID detectors measure the output state, including qubit-qubit correlations. We determined the gate's truth table by directly measuring the state transfer amplitudes and by acquiring the relevant quantum phase shift using a Ramsey-like interference experiment. The four conditional gates result from the symmetry of the qubits in the pair: either qubit can assume the role of control or target, and the gate action can be conditioned on either the 0-state or the 1-state. These gates are now sufficiently characterized to be used in quantum algorithms, and together form an efficient set of versatile building blocks.

Entanglement and Bell states in superconducting flux qubits

We theoretically study macroscopic quantum entanglement in two superconducting flux qubits. To manipulate the state of two flux qubits, a Josephson junction is introduced in the connecting loop coupling the qubits. Increasing the coupling energy of the Josephson junction makes it possible to achieve relatively strong coupling between the qubits, causing two-qubit tunneling processes to be even dominant over the single-qubit tunneling processes in the states of two qubits. It is shown that due to the two-qubit tunneling processes, both the ground state and excited states of the coupled flux qubits can be a Bell type of maximally entangled state, in experimentally accessible regimes. The parameter regimes for the Bell states are discussed in terms of magnetic flux and Josephson coupling energies.

Spectroscopy of three strongly coupled flux qubits

We have carried out spectroscopic measurements of a system of three strongly coupled four-junction flux qubits. The samples studied cover a wide range of parameters with the coupling energy between neighboring qubits varying between 0.75 GHz and 6.05 GHz. The observed complicated spectra agree well with eight-level theory. The experiments are relevant for the realization of a tunable coupling between qubits.

Generalized switchable coupling for superconducting qubits using double resonance

We propose a method for switchable coupling between superconducting qubits using double resonance. The inter-qubit coupling is achieved by applying near-resonant oscillating fields to the two qubits. The deviation from resonance relaxes the criterion of strong driving fields while still allowing for a fully entangling two-qubit gate. This method avoids some of the shortcomings of previous proposals for switchable coupling. We discuss the possible application of our proposal to a pair of inductively coupled flux qubits, and we consider the extension to phase qubits.

Superconducting system for adiabatic quantum computing

We study the Hamiltonian of a system of inductively coupled flux qubits, which has been theoretically proposed for adiabatic quantum computation to handle NP problems. We study the evolution of a basic structure consisting of three coupled rf-SQUIDs upon tuning the external flux bias, and we show that the adiabatic nature of the evolution is guaranteed by the presence of the single-SQUID gap. We further propose a scheme and the first realization of an experimental device suitable for verifying the theoretical results.

Observation of excitation in asymmetric flux qubits coupled inductively

We measured magnetic flux produced by coupled flux qubits with a switching current measurement of a DC-SQUID. Both the circulating currents and the SQUID–qubit coupling were designed to be asymmetric. The experimental result exhibits a broad peak and dip, and does not agree with the thermally averaged magnetic flux calculated with the two qubit Hamiltonian. This disagreement can be explained in terms of nonthermal excitation of the coupled qubits, which is probably caused by the microwaves generated by the DC-SQUID in the voltage state.

A multi-qubit system for a scalable adiabatic quantum evolution

We study the Hamiltonian of a system of inductively coupled flux qubits, which has been theoretically proposed for adiabatic quantum computation to handle NP problems. We study the evolution of a basic structure consisting of three coupled rf-SQUIDs upon tuning the external flux bias, and we show that the adiabatic nature of the evolution is guaranteed by the presence of the single-SQUID gap. We further propose an experiment to study the problem of scaling up the number of coupled qubits guaranteeing the adiabatic nature of the process.

Quantum Entanglement and Controlled Logical Gates Using Coupled SQUID Flux Qubits

We present an approach to realize universal two-bit quantum gates using two SQUID flux qubits. In this approach the basic unit consists of two inductively coupled SQUIDs with realistic device parameters. Quantum logical gates are implemented by applying resonant microwave pulse to the qubits. This procedure is demonstrated by realizing a controlled-NOT (CNOT) gate and the maximally entangled states of the coupled qubits through highly accurate numerical solution of the time-dependent Schrodinger equation of the system. This coupling scheme is simple and can be readily extended to many-qubit circuits required for scalable quantum information processing.

Spectroscopy on Two Coupled Superconducting Flux Qubits

We have performed spectroscopy measurements on two coupled flux qubits. The qubits are coupled inductively, which results in a sigma(z)(1)sigma(z)(2) interaction. By applying microwave radiation, we observe resonances due to transitions from the ground state to the first two excited states. From the position of these resonances as a function of the applied magnetic field, we observe the coupling of the qubits. The coupling strength agrees with calculations of the mutual inductance.

Hamiltonian for coupled flux qubits

An effective Hamiltonian is derived for two coupled three-Josephson-junction (3JJ) qubits. This is not quite trivial, for the customary "free" 3JJ Hamiltonian is written in the limit of zero inductance L. Neglecting the self-flux is already dubious for one qubit when it comes to readout, and becomes untenable when discussing inductive coupling. First, inductance effects are analyzed for a single qubit. For small L, the self-flux is a "fast variable" which can be eliminated adiabatically. However, the commonly used junction phases are_not_ appropriate "slow variables", and instead one introduces degrees of freedom which are decoupled from the loop current to leading order. In the quantum case, the zero-point fluctuations (LC oscillations) in the loop current diverge as L->0. Fortunately, they merely renormalize the Josephson couplings of the effective (two-phase) theory. In the coupled case, the strong zero-point fluctuations render the full (six-phase) wave function significantly entangled in leading order. However, in going to the four-phase theory, this uncontrollable entanglement is integrated out completely, leaving a computationally usable mutual-inductance term of the expected form as the effective interaction.

Fast two-bit operations in inductively coupled flux qubits

A central problem for implementing efficient quantum computing is how to realize fast operations (both one- and two-bit ones). However, this is difficult to achieve for a collection of qubits, especially for those separated far away, because the interbit coupling is usually much weaker than the intrabit coupling. Here we present an experimentally feasible method to effectively couple two flux qubits via a common inductance and treat both single and coupled flux qubits with more realistic models which include the loop inductance. The main advantage of our proposal is that a strong interbit coupling can be achieved using a small inductance, so that two-bit operations as fast as one-bit ones can be easily realized. We also show the flux dependence of the transitions between states for the coupled flux qubits.

Publisher's Note: Evidence for Entangled States of Two Coupled Flux Qubits [Phys. Rev. Lett.93, 037003 (2004)

Publisher's Note: Evidence for Entangled States of Two Coupled Flux Qubits [Phys. Rev. Lett.<b>93</b>, 037003 (2004)

Evidence for entangled states of two coupled flux qubits.

We have studied the low-frequency magnetic susceptibility of two inductively coupled flux qubits using the impedance measurement technique (IMT), through their influence on the resonant properties of a weakly coupled high-quality tank circuit. In a single qubit, an IMT dip in the tank's current-voltage phase angle at the level anticrossing yields the amplitude of coherent flux tunneling. For two qubits, the difference (IMT deficit) between the sum of single-qubit dips and the dip amplitude when both qubits are at degeneracy shows that the system is in a mixture of entangled states (a necessary condition for entanglement). The dependence on temperature and relative bias between the qubits allows one to determine all the parameters of the effective Hamiltonian and equilibrium density matrix, and confirms the formation of entangled eigenstates.