Quantum

Frustration-free control for quantum-state preparation: an exact first-passage theory

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Briefings

A new exact first-passage theory describes how quantum circuits using local measurements and feedback prepare Dicke states of N_q qubits. The theory shows the dynamics close exactly to a classical process involving N_q(N_q-1)/2 singlet-pair projectors, reducing a large many-body Liouvillian to a polynomial-size generator. In one dimension, the slowest relaxation rate is 2[1-cos(pi/N_q)] in units of the measurement rate, and the relaxation time is bounded below by the inverse fraction of pair configurations where feedback acts.

Key points

• The theory provides an exact first-passage description for preparing Dicke states of N_q qubits using local measurements and feedback.
• The relaxation time is bounded below by the inverse fraction of pair configurations on which feedback acts, requiring at least linear time in N_q.

Context

Quantum circuits based on local measurements and feedback can autonomously prepare and stabilize entangled many-body states. This research develops an exact theory for the preparation of Dicke states, which span the permutation-symmetric subspace, using local singlet projectors to define constraints.

Limitations

The study is limited to one dimension and focuses on the exact closure of the dynamics for Dicke states. It does not address extensions to modified transport, restricted feedback, or physical errors, nor does it provide data on ensemble fluctuations beyond the second-moment closure.

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