Superconducting flux qubits with three Josephson junctions are promising candidates for the building blocks of a quantum computer. We have applied the imaginary time evolution method to study the model of this qubit accurately by calculating its wavefunctions and eigenenergies. Because such qubits are manipulated with magnetic flux microwave pulses, they might be irradiated into non-computational states, which is called the leakage effect. By the evolution of the density matrix of the qubit under either hard-shaped π-pulse or Gaussian-shaped π-pulse to carry out quantum NOT operation, it has been demonstrated that the leakage effect for a flux qubit is very small even for hard-shaped microwave pulses while Gaussian-shaped pulses may suppress the leakage effect to a negligible level.Superconducting flux qubits with three Josephson junctions are promising candidates for the building blocks of a quantum computer. We have applied the imaginary time evolution method to study the model of this qubit accurately by calculating its wavefunctions and eigenenergies. Because such qubits are manipulated with magnetic flux microwave pulses, they might be irradiated into non-computational states, which is called the leakage effect. By the evolution of the density matrix of the qubit under either hard-shaped π-pulse or Gaussian-shaped π-pulse to carry out quantum NOT operation, it has been demonstrated that the leakage effect for a flux qubit is very small even for hard-shaped microwave pulses while Gaussian-shaped pulses may suppress the leakage effect to a negligible level.

arXiv:cond-mat/0511012Chinese Physics LettersMar 30, 20066 citations

Multilevel quantum description of decoherence in superconducting qubits

Guido Burkard, R. H. Koch, David Peter Divincenzo

We present a multilevel quantum theory of decoherence for a general circuit realization of a superconducting qubit. Using electrical network graph theory, we derive a Hamiltonian for the circuit. The dissipative circuit elements (external impedances, shunt resistors) are described using the Caldeira-Leggett model. The master equation for the superconducting phases in the Born-Markov approximation is derived and brought into the Bloch-Redfield form in order to describe multilevel dissipative quantum dynamics of the circuit. The model takes into account leakage effects, i.e., transitions from the allowed qubit states to higher excited states of the system. As a special case, we truncate the Hilbert space and derive a two-level (Bloch) theory with characteristic relaxation ${(T}_{1})$ and decoherence ${(T}_{2})$ times. We apply our theory to the class of superconducting flux qubits; however, the formalism can be applied for both superconducting flux and charge qubits.We present a multilevel quantum theory of decoherence for a general circuit realization of a superconducting qubit. Using electrical network graph theory, we derive a Hamiltonian for the circuit. The dissipative circuit elements (external impedances, shunt resistors) are described using the Caldeira-Leggett model. The master equation for the superconducting phases in the Born-Markov approximation is derived and brought into the Bloch-Redfield form in order to describe multilevel dissipative quantum dynamics of the circuit. The model takes into account leakage effects, i.e., transitions from the allowed qubit states to higher excited states of the system. As a special case, we truncate the Hilbert space and derive a two-level (Bloch) theory with characteristic relaxation ${(T}_{1})$ and decoherence ${(T}_{2})$ times. We apply our theory to the class of superconducting flux qubits; however, the formalism can be applied for both superconducting flux and charge qubits.

arXiv:cond-mat/0308025Physical Review BFeb 11, 2004175 citations

On the Quantum Measurement of Superconducting Flux Qubits

Thomas Picot

Sep 22, 20100 citations

Intrinsic leakage of the Josephson flux qubit and breakdown of the two-level approximation for strong driving

Alejandro Ferrón, Daniel Domı́nguez

Solid-state devices for quantum-bit computation (qubits) are not perfect isolated two-level systems since additional higher energy levels always exist. One example is the Josephson flux qubit, which consists on a mesoscopic superconducting quantum interference device loop with three Josephson junctions operated at or near a magnetic flux of half quantum. We study intrinsic leakage effects, i.e., direct transitions from the allowed qubit states to higher excited states of the system during the application of pulses for quantum computation operations. The system is started in the ground state and rf-magnetic field pulses are applied at the qubit resonant frequency with pulse intensity ${f}_{p}$ . A perturbative calculation of the average leakage for small ${f}_{p}$ is performed for this case, obtaining that the leakage is quadratic in ${f}_{p}$ , and that it depends mainly on the matrix elements of the supercurrent. Numerical simulations of the time-dependent Schr\"odinger equation corresponding to the full Hamiltonian of this device were also performed. From the simulations we obtain the value of ${f}_{p}$ above which the two-level approximation breaks down, and we estimate the maximum Rabi frequency that can be achieved. We study the leakage as a function of the ratio $\ensuremath{\alpha}$ among the Josephson energies of the junctions of the device, obtaining the best value for minimum leakage $(\ensuremath{\alpha}\ensuremath{\approx}0.85)$. The effects of flux noise on the leakage are also discussed.Solid-state devices for quantum-bit computation (qubits) are not perfect isolated two-level systems since additional higher energy levels always exist. One example is the Josephson flux qubit, which consists on a mesoscopic superconducting quantum interference device loop with three Josephson junctions operated at or near a magnetic flux of half quantum. We study intrinsic leakage effects, i.e., direct transitions from the allowed qubit states to higher excited states of the system during the application of pulses for quantum computation operations. The system is started in the ground state and rf-magnetic field pulses are applied at the qubit resonant frequency with pulse intensity ${f}_{p}$. A perturbative calculation of the average leakage for small ${f}_{p}$ is performed for this case, obtaining that the leakage is quadratic in ${f}_{p}$, and that it depends mainly on the matrix elements of the supercurrent. Numerical simulations of the time-dependent Schr\"odinger equation corresponding to the full Hamiltonian of this device were also performed. From the simulations we obtain the value of ${f}_{p}$ above which the two-level approximation breaks down, and we estimate the maximum Rabi frequency that can be achieved. We study the leakage as a function of the ratio $\ensuremath{\alpha}$ among the Josephson energies of the junctions of the device, obtaining the best value for minimum leakage $(\ensuremath{\alpha}\ensuremath{\approx}0.85)$. The effects of flux noise on the leakage are also discussed.

arXiv:0910.5640Physical Review BMar 8, 201025 citations

{(T}_{1})

and decoherence

{(T}_{2})

times. We apply our theory to the class of superconducting flux qubits; however, the formalism can be applied for both superconducting flux and charge qubits.

{f}_{p}

. A perturbative calculation of the average leakage for small

{f}_{p}

is performed for this case, obtaining that the leakage is quadratic in

{f}_{p}

, and that it depends mainly on the matrix elements of the supercurrent. Numerical simulations of the time-dependent Schr\"odinger equation corresponding to the full Hamiltonian of this device were also performed. From the simulations we obtain the value of

{f}_{p}

above which the two-level approximation breaks down, and we estimate the maximum Rabi frequency that can be achieved. We study the leakage as a function of the ratio $\ensuremath{\alpha}$ among the Josephson energies of the junctions of the device, obtaining the best value for minimum leakage $(\ensuremath{\alpha}\ensuremath{\approx}0.85)$. The effects of flux noise on the leakage are also discussed.