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SUMMARY:Efficient LCU Block Encodings through Dicke State Preparation - Ro
 el Van Beeumen\, Lawrence Berkeley National Laboratory and KU Leuven
DTSTART:20260219T123000Z
DTEND:20260219T140000Z
UID:TALK242965@talks.cam.ac.uk
CONTACT:Lila Cadi Tazi
DESCRIPTION:With Quantum Singular Value Transformation (QSVT) emerging as 
 a unifying framework for diverse quantum speedups\, efficient construction
  of block encodings—its fundamental input model—has become increasing
 ly crucial. However\, devising explicit block-encoding circuits has remain
 ed a significant challenge. A general strategy is the Linear Combination 
 of Unitaries (LCU) method\, though its practical utility is often limited 
 by substantial gate overhead. To address this\, we introduce the Fast One
 -Qubit-Controlled Select LCU (FOQCS-LCU)\, a compact formulation that req
 uires only a linear number of ancilla qubits and admits explicit decomposi
 tions into one- and two-qubit gates. By exploiting Hamiltonian structure\
 , we design a parametrized family of efficient Dicke-state preparation rou
 tines that enable systematic construction of state-preparation oracles at
  greatly reduced gate cost. The check-matrix formalism further yields a co
 nstant-depth SELECT oracle implemented as two fully parallelizable layers
  of singly controlled Pauli gates. We also present explicit block-encodin
 g circuits for matrix polynomial transformations and show that the additio
 nal circuit-depth overhead scales linearly in the polynomial degree d\, 
 independent of system size or the cost of encoding the original matrix alo
 ne. Moreover\, both the FOQCS-LCU circuits and their associated polynomia
 l transformations can be controlled with negligible overhead\, enabling ef
 ficient applications such as Hadamard tests. We construct explicit implem
 entations for representative spin models\, including Heisenberg and spin-g
 lass Hamiltonians\, and provide detailed non-asymptotic gate counts. Nume
 rical benchmarks demonstrate over an order-of-magnitude reduction in CNOT 
 count compared to conventional LCU approaches\, establishing a practical 
 route to low-depth block encodings for a broad class of structured matrice
 s.
LOCATION:Room U203\, Cybercafe\, Yusuf Hamied Department of Chemistry\, Ca
 mbridge
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