Dicke-state preparation through global transverse control of
Ising-coupled qubits
- URL: http://arxiv.org/abs/2302.12483v3
- Date: Fri, 7 Jul 2023 14:35:30 GMT
- Title: Dicke-state preparation through global transverse control of
Ising-coupled qubits
- Authors: Vladimir M. Stojanovic, Julian K. Nauth
- Abstract summary: We consider the problem of engineering the two-excitation Dicke state $|D3_2rangle$ in a three-qubit system with all-to-all Ising-type qubit-qubit interaction.
For the sake of illustration, we describe the preparation of the two-excitation Dicke state $|D4_2rangle$ in a four-qubit system.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We consider the problem of engineering the two-excitation Dicke state
$|D^{3}_{2}\rangle$ in a three-qubit system with all-to-all Ising-type
qubit-qubit interaction, which is also subject to global transverse
(Zeeman-type) control fields. The theoretical underpinning for our envisioned
state-preparation scheme, in which $|000\rangle$ is adopted as the initial
state of the system, is provided by a Lie-algebraic result that guarantees
state-to-state controllability of this system for an arbitrary choice of
initial- and final states that are invariant with respect to permutations of
qubits. This scheme is envisaged in the form of a pulse sequence that involves
three instantaneous control pulses, which are equivalent to global qubit
rotations, and two Ising-interaction pulses of finite durations between
consecutive control pulses. The design of this pulse sequence (whose total
duration is $T\approx 0.95\:\hbar/J$, where $J$ is the Ising-coupling strength)
leans heavily on the concept of the symmetric sector, a four-dimensional,
permutationally-invariant subspace of the three-qubit Hilbert space. We
demonstrate the feasibility of the proposed state-preparation scheme by
carrying out a detailed numerical analysis of its robustness to systematic
errors, i.e. deviations from the optimal values of the eight parameters that
characterize the underlying pulse sequence. Finally, we discuss how our
proposed scheme can be generalized for engineering Dicke states in systems with
$N \ge 4$ qubits. For the sake of illustration, we describe the preparation of
the two-excitation Dicke state $|D^{4}_{2}\rangle$ in a four-qubit system.
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