We introduce a new exact classical sampling algorithm for Clifford+T circuits, called T-by-T sampling. For a circuit with T-count t, it reduces sampling to evaluating 2t amplitudes of circuits with successively increasing T-counts 1,2,...,t, without the need to compute costly marginal probabilities. Crucially, the number of amplitude evaluations is completely independent of the surrounding Clifford structure. This makes T-by-T sampling well suited for use together with low-rank stabiliser decompositions, which enable efficient amplitude evaluations as long as the T-count is not too high. In that sense, T-by-T sampling is an improvement over the gate-by-gate sampling technique introduced by Bravyi, Gosset, and Liu (Phys. Rev. Lett. 128, 2022), where the number of amplitudes instead scales with the number of non-monomial operations such as Hadamard gates, which can remain large even in circuits with low stabiliser rank. Concretely, T-by-T sampling offers significant speedups in regimes where T gates are embedded within large Clifford computations. This makes it well suited for applications such as simulating quantum error correction experiments, which typically have lower T complexity but involve extensive Clifford operations and measurements. In particular, we show how T-by-T sampling allows us to take samples from recent end-to-end magic state cultivation circuits with escape up to distance 19 in a couple of seconds.
We propose an algorithm that can synthesize circuits to gate sets consisting of a 2n-arity Clifford gate and arbitrary single qubit rotations. To do this, we represent the circuit as a sequence of Pauli gadgets and jointly synthesize them by placing the multi-qubit Clifford in the synthesized circuit and pushing its adjoint through the remaining gadgets such that some qubits are disconnected from some gadgets. The pushed gadgets are collected in a Clifford tableau, which is decomposed afterwards. With the help of our algorithm we run experiments where we synthesize circuits to varying sizes of target multi-qubit gates. These experiments indicate that increases in gate size can lead to smaller output circuits, and that different connectivity constraints have meaningful differences in how higher arity gates effect the circuit sized.
Controlled subcircuits are commonplace in quantum algorithms as they represent the quantum analogue of branching statements (if then). We introduce a generalization of controlled subcircuits in the form of a binary operation which sends pairs of unitary quantum circuits to a generalized controlled operation, whose semantics are based on matrix exponentials and logarithms. The family of quantum circuits with generalized controlled operations and circuit exponentiation is denoted HQC for Hierarchical Quantum Circuits. We formalize HQC as a modified prop category using a novel category-theoretic construction, and provide a sound and complete equational theory for diagrammatic reasoning in HQC.
This volume contains the proceedings of the 23rd International Conference on Quantum Physics and Logic (QPL 2026), which was held from August 17 to August 21 2026, in Amsterdam, The Netherlands, organized by the University of Amsterdam. QPL is an annual conference that brings together academic and industry researchers working on topics ranging from basic research in the foundations of physics to applications in quantum computing and communication, both for near-term quantum hardware and future large-scale, fault-tolerant devices. The conference places particular emphasis on the application of formal algebraic, logical, compositional, and categorical structures to quantum theory and related areas. Work applying quantum-inspired techniques and structures to other fields such as (classical) computation, linguistics, artificial intelligence, and causality is also welcome.
