arXiv subjects

Samuel H. Pickering

Publications and source records attributed to Samuel H. Pickering.

3 recordsLinked to original sources

arXiv2026

Solvable Quantum Circuits with non-Markovian Influence Matrices

Influence matrices encode the action exerted on local subsystems by the rest of an extended quantum many-body system during their evolution. Thus, knowledge of the influence matrix facilitates computationally efficient simulations of local dynamics. Here we propose a new systematic approach to generating quantum circuits with complex dynamics for which the influence matrices can be written down exactly. In contrast to previous frameworks of this kind, such as dual-unitary circuits, the resulting influence matrices are non-Markovian, exhibiting nontrivial temporal correlations. We explicitly construct a broad family of circuits of this kind, based on dressing free-fermion (matchgate) circuits with appropriately chosen interaction terms. We show that, contrary to previous solvable instances, these circuits produce patterns of correlations that closely resemble that of typical many-body systems. Our approach can be directly interpreted in terms of an error correction scheme where the terms breaking the solvability of the influence matrices play the role of errors.

cond-mat.stat-mech↗

arXiv2026

Asymptotically Solvable Quantum Circuits

The discovery of chaotic quantum circuits with (partially) solvable dynamics has played a key role in our understanding of non-equilibrium quantum matter and, at the same time, has helped the development of concrete platforms for quantum computation. It was shown that solvability does not prevent the generation of chaotic dynamics, however, it imposes non-trivial constraints on the generated correlations. A natural question is then whether it is possible to gain insight into the generic case despite the latter being very hard to access. To address this question here we introduce a family of 'asymptotically solvable' quantum circuits where the solvability constraints only affect correlations on length scales beyond a tuneable threshold. This means that their dynamics are only solvable for long enough times: for times shorter than the threshold they are generic. We show this by computing both their dynamical correlations on the equilibrium (infinite temperature) state and their thermalisation dynamics following quantum quenches from compatible (asymptotically solvable) non-equilibrium initial states. The class of systems we introduce is generically ergodic but contains a non-interacting point, which we use to provide exact analytical results, complementing those of numerical experiments, on the non-solvable early time regime.

cond-mat.stat-mech↗

arXiv2024

Phase transitions in full counting statistics of free fermions and directed polymers

We consider directed polymers in 1+1 spatial dimension under action of an external repulsive potential along a line. Using the exact mapping onto imaginary time evolution of free fermions we find that for sufficiently strong potential the system of polymers undergoes a continuous configurational phase transition. The transition corresponds to merging empty regions in the dominant limit shape.

cond-mat.stat-mech↗