30 research outputs found
Continuous joint measurement and entanglement of qubits in remote cavities
We present a first-principles theoretical analysis of the entanglement of two
superconducting qubits in spatially separated microwave cavities by a
sequential (cascaded) probe of the two cavities with a coherent mode, that
provides a full characterization of both the continuous measurement induced
dynamics and the entanglement generation. We use the SLH formalism to derive
the full quantum master equation for the coupled qubits and cavities system,
within the rotating wave and dispersive approximations, and conditioned
equations for the cavity fields. We then develop effective stochastic master
equations for the dynamics of the qubit system in both a polaronic reference
frame and a reduced representation within the laboratory frame. We compare
simulations with and analyze tradeoffs between these two representations,
including the onset of a non-Markovian regime for simulations in the reduced
representation. We provide conditions for ensuring persistence of entanglement
and show that using shaped pulses enables these conditions to be met at all
times under general experimental conditions. The resulting entanglement is
shown to be robust with respect to measurement imperfections and loss channels.
We also study the effects of qubit driving and relaxation dynamics during a
weak measurement, as a prelude to modeling measurement-based feedback control
in this cascaded system.Comment: 17 pages, 8 figures. Published versio
Controlling Quantum Information Devices
Quantum information and quantum computation are linked by a common mathematical and physical framework of quantum mechanics. The manipulation of the predicted dynamics and its optimization is known as quantum control. Many techniques, originating in the study of nuclear magnetic resonance, have found common usage in methods for processing quantum information and steering physical systems into desired states. This thesis expands on these techniques, with careful attention to the regime where competing effects in the dynamics are present, and no semi-classical picture exists where one effect dominates over the others. That is, the transition between the diabatic and adiabatic error regimes is examined, with the use of such techniques as time-dependent diagonalization, interaction frames, average-Hamiltonian expansion, and numerical optimization with multiple time-dependences. The results are applied specifically to superconducting systems, but are general and improve on existing methods with regard to selectivity and crosstalk problems, filtering of modulation of resonance between qubits, leakage to non-compuational states, multi-photon virtual transitions, and the strong driving limit
Charting the circuit QED design landscape using optimal control theory
With recent improvements in coherence times, superconducting transmon qubits
have become a promising platform for quantum computing. They can be flexibly
engineered over a wide range of parameters, but also require us to identify an
efficient operating regime. Using state-of-the-art quantum optimal control
techniques, we exhaustively explore the landscape for creation and removal of
entanglement over a wide range of design parameters. We identify an optimal
operating region outside of the usually considered strongly dispersive regime,
where multiple sources of entanglement interfere simultaneously, which we name
the quasi-dispersive straddling qutrits (QuaDiSQ) regime. At a chosen point in
this region, a universal gate set is realized by applying microwave fields for
gate durations of 50 ns, with errors approaching the limit of intrinsic
transmon coherence. Our systematic quantum optimal control approach is easily
adapted to explore the parameter landscape of other quantum technology
platforms.Comment: 13 pages, 5 figures, 2 pages supplementary, 1 supplementary figur
Non-perturbative analytical diagonalization of Hamiltonians with application to coupling suppression and enhancement in cQED
Deriving effective Hamiltonian models plays an essential role in quantum
theory, with particular emphasis in recent years on control and engineering
problems. In this work, we present two symbolic methods for computing effective
Hamiltonian models: the Non-perturbative Analytical Diagonalization (NPAD) and
the Recursive Schrieffer-Wolff Transformation (RSWT). NPAD makes use of the
Jacobi iteration and works without the assumptions of perturbation theory while
retaining convergence, allowing to treat a very wide range of models. In the
perturbation regime, it reduces to RSWT, which takes advantage of an in-built
recursive structure where remarkably the number of terms increases only
linearly with perturbation order, exponentially decreasing the number of terms
compared to the ubiquitous Schrieffer-Wolff method. In this regime, NPAD
further gives an exponential reduction in terms, i.e. superexponential compared
to Schrieffer-Wolff, relevant to high precision expansions. Both methods
consist of algebraic expressions and can be easily automated for symbolic
computation. To demonstrate the application of the methods, we study the ZZ and
cross-resonance interactions of superconducting qubits systems. We investigate
both suppressing and engineering the coupling in near-resonant and
quasi-dispersive regimes. With the proposed methods, the coupling strength in
the effective Hamiltonians can be estimated with high precision comparable to
numerical results.Comment: 19 pages, 8 figures, with more examples for NPAD including
cross-resonanc