Related papers: Average-case quantum complexity from glassiness
The states of an open quantum system interact ("talk") with one another via the extended environment into which the localized system is embedded. This interaction is mediated by the source term of the Schr\"odinger equation which describes…
In a closed single-particle quantum system, spatial disorder induces Anderson localization of eigenstates and halts wave propagation. The phenomenon is vulnerable to interaction with environment and decoherence, that is believed to restore…
Starting from a many-body classical system governed by a trace-form entropy we derive, in the stochastic quantization picture, a family of non linear and non-Hermitian Schroedinger equations describing, in the mean filed approximation, a…
Run-times of quantum algorithms are often studied via an asymptotic, worst-case analysis. Whilst useful, such a comparison can often fall short: it is not uncommon for algorithms with a large worst-case run-time to end up performing well on…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
The slow relaxation and aging of glassy systems can be modelled as a Markov process on a simplified rough energy landscape: energy minima where the system tends to get trapped are taken as nodes of a random network, and the dynamics are…
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years the replica-symmetry-breaking mean field theory of spin glasses and the…
The eigenspectrum of a non-normal matrix, which does not commute with its Hermitian conjugate, is a central issue of non-Hermitian physics that has been extensively studied in the past few years. There is, however, another characteristic of…
Quantum computation is frequently mischaracterized as the simultaneous execution of exponentially many classical computations. This article offers a conceptual clarification of why this ``branchwise parallelism'' picture is misleading,…
Physical laws for elementary particles can be described by the quantum dynamics equation given a Hamiltonian. The solution are probability amplitudes in Hilbert space that evolve over time. A probability density function over position and…
The standard stabilizer formalism provides a setting to show that quantum computation restricted to operations within the Clifford group are classically efficiently simulable: this is the content of the well-known Gottesman-Knill theorem.…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
Understanding how classical physics emerges from quantum mechanics remains a central problem in the foundations of physics. Here we derive a classical limit from finite-resolution measurements, modeled by continuous coarse-grained POVMs.…
Classical simulation of quantum systems plays an important role in the study of many-body phenomena and in the benchmarking and verification of quantum technologies. Exact simulation is often limited to small systems because the dimension…
Boundary time crystals exhibit measurement-induced phase transitions in their steady-state entanglement, with critical behavior that depends on the particular unraveling of the Lindblad dynamics. In this work, we investigate another key…
We explore the transient dynamics associated with the emergence of the classical signal in the full quantum system. We start our study from the instability which promotes the squeezing of the quantum system. This is often interpreted as the…
Despite the enormous theoretical and application interests, a fundamental understanding of the glassy dynamics remains elusive. The static properties of glassy and ordinary liquids are similar, but their dynamics are dramatically different.…
Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and the fact that unitary transformations on that Hilbert space can be broken down to universal gates that act only on one or two…
Using molecular dynamics simulation, we investigate the slow dynamics of a supercooled binary mixture of soft particles interacting with a generalized Hertzian potential. At low density, it displays typical slow dynamics near its glass…
In the previous parts of this work, we established the Prequantum Groupoid $\mathbf{T}_\omega$ as the universal geometric container for quantum mechanics. This approach, which we call the "Geometric Quantization by Paths" (GQbP) framework,…