arXiv subjects

Luna Lima Keller

Publications and source records attributed to Luna Lima Keller.

3 recordsLinked to original sources

arXiv2026

(A Variant of) Clifford Circuit Synthesis is NP-Complete

Optimal circuit synthesis is the problem of finding the shortest-depth circuit representation of a given functionality with respect to a pre-specified elementary gate set. This is a central problem in both quantum and classical hardware design. While the classical version is very well understood -- both in terms of heuristics and rigorous hardness assertions -- much less is known about optimal quantum circuit synthesis. We focus on optimal Clifford circuit synthesis, for which various heuristics are known, e.g. via reduction to 3-SAT. Our main result supplies a matching hardness result: a variant of optimal Clifford synthesis is NP-hard. The proof proceeds in two parts: (i) reduce 3-edge colorability on 3-regular graphs to a circuit synthesis problem that only involves CZ gates, (ii) prove that the availability of additional elementary Clifford gates -- most notably: Hadamard, phase and CNOT -- cannot lead to further improvements of the optimal circuit depth. Our work sharpens the complexity-theoretic understanding of Clifford circuits: simulation and equivalence checking are in P, whereas deciding whether a Clifford unitary admits an implementation within a prescribed depth is NP-complete.

quant-ph↗

arXiv2026

Every Little Thing Heat Does Is Magic

How can one certify that an unknown quantum state possesses magic without resorting to full state tomography? We address this question by introducing two thermodynamic witnesses that rely solely on energy and heat measurements. First, we define the stabilizer ground-state energy as the lowest energy achievable by any stabilizer state, and the stabilizer gap as the separation between this value and the true ground-state energy. Any state whose energy lies below the stabilizer ground-state energy is therefore necessarily nonstabilizer. This leads to a direct witness of magic using only average-energy measurements. To overcome the limitations when direct energy measurements are inconclusive, we further develop a nonlinear witness based on heat exchange with a thermal ancilla. Specifically, we derive fundamental bounds on heat that are satisfied by all stabilizer states; therefore, their violation certifies the presence of magic. We demonstrate the effectiveness of our approach through several examples, ranging from few-body systems where heat exchange reveals nonstabilizerness even when energy measurements alone fail, to the transverse-field Ising chain, where the stabilizer gap becomes maximal at the quantum critical point.

quant-ph↗

arXiv2026

Two-particle scattering on general graphs

Quantum walks in general graphs, or more specifically scattering on graphs, encompass enough complexity to perform universal quantum computation. Any given quantum circuit can be broken down into single- and two-qubit gates, which can then be translated into subgraphs -- gadgets -- that implement such unitaries on the logical qubits, simulated by particles traveling along a sparse graph. In this work, we start to develop a full theory of multi-particle scattering on graphs and give initial applications to build multi-particle gadgets with different properties.

quant-ph↗