A hardware-efficient binary-tree ansatz has a closed-form diagonal Fubini–Study metric, enabling metric-aware VQE and time evolution without auxiliary circuits, with linear-in-k pruning for sparse sectors.
Optimal Circuit Size for Fixed-Hamming-Weight Quantum States Preparation
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abstract
We study the problem of efficiently preparing fixed-Hamming-weight (HW-$k$) quantum states, which are superpositions of $n$-qubit computational basis states with exactly $k$ ones. We present a quantum circuit construction that prepares any $n$-qubit HW-$k$ state with a circuit size of $O(\binom{n}{k})$ using at most $\max\{0, n-3\}$ ancillary qubits. This is the first construction that achieves the theoretical lower bound on circuit size while using only a small number of ancillary qubits. We believe that the techniques presented in this work can be extended to other quantum state preparation algorithms based on decision diagrams, potentially reducing the reliance on ancillary qubits or lowering the overall circuit size.
fields
quant-ph 2years
2026 2representative citing papers
A deterministic algorithm prepares arbitrary multi-qudit states in a definite-weight subspace via Gray-code ordering of multiset permutations, reducing preparation to controlled 2-qudit Gray rotations, and is demonstrated on Bethe states of the SU(3) Heisenberg model and SU(d) Dicke states.
citing papers explorer
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A hardware-efficient variational ansatz with an exact diagonal metric for real- and imaginary-time evolution and Haar sampling
A hardware-efficient binary-tree ansatz has a closed-form diagonal Fubini–Study metric, enabling metric-aware VQE and time evolution without auxiliary circuits, with linear-in-k pruning for sparse sectors.
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Preparing multi-qudit states in a definite-weight subspace
A deterministic algorithm prepares arbitrary multi-qudit states in a definite-weight subspace via Gray-code ordering of multiset permutations, reducing preparation to controlled 2-qudit Gray rotations, and is demonstrated on Bethe states of the SU(3) Heisenberg model and SU(d) Dicke states.