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In this paper, using 1+1D models as examples, we study symmetries and anomalous symmetries via multi-component partition functions obtained through symmetry twists, and their transformations under the mapping class group of spacetime. This…
One-to-one reversible automata are introduced. Their applicability to a modelling of the quantum mechanical measurement process is discussed.
As quantum devices scale up, many-body quantum gates and algorithms begin to surpass what is possible to simulate classically. Validation methods which rely on such classical simulation, such as process tomography and randomized…
Conformal symmetry heavily constrains the dynamics of non-relativistic quantum gases tuned to a nearby quantum critical point. One important consequence of this symmetry is that entropy production can be absent in far away from equilibrium…
Simulating quantum systems with their environments often requires non-unitary operations, and mapping these to quantum devices often involves expensive dilations or prohibitive measurement costs to achieve desired precisions. Building on…
Quantum mechanical unitarity in our universe is challenged both by the notion of the big bang, in which nothing transforms into something, and the expansion of space, in which something transforms into more something. This motivates the…
Time reversal in a macroscopic system is contradicting daily experience. It is practically impossible to restore a shattered cup to its original state by just time reversing the microscopic dynamics that led to its breakage. Yet, with the…
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…
Quantum devices featuring mid-circuit measurement and reset capabilities, such as quantum computers and dual-species Rydberg quantum simulators, enable the realization of quantum cellular automata. These systems evolve in discrete time…
We develop a framework for simulating measure-preserving, ergodic dynamical systems on a quantum computer. Our approach provides a new operator-theoretic representation of classical dynamics by combining ergodic theory with quantum…
A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational…
Quantum physics involves an ensemble of quantum systems, usually one thinks of a large ensemble of identical quantum systems at one single time. In single ion experiments one has a single quantum system at an ensemble of different times.…
A proof is given that an invertible and a unitary operator can be used to reproduce the effect of a q-deformed commutator of annihilation and creation operators. In other words, the original annihilation and creation operators are mapped…
Driven-dissipative quantum systems generically do not satisfy simple notions of detailed balance based on the time symmetry of correlation functions. We show that such systems can nonetheless exhibit a hidden time-reversal symmetry which…
Theories described by non-Hermitian Hamiltonians are known to possess strictly positive energy eigenvalues and exhibit unitary time evolution if the Hamiltonian is symmetric under discrete parity and time (PT) transformation. In this work,…
Starting from a semiclassical approach recently developed for spectral correlation functions of quantum systems whose classical dynamics is chaotic, we focus on the case of broken time-reversal symmetry, the so-called unitary class. We…
Processes such as quantum computation, or the evolution of quantum cellular automata are typically described by a unitary operation implemented by an external observer. In particular, an interaction is generally turned on for a precise…
We introduce the novel class $(E_\alpha)_{\alpha \in [-\infty,1)}$ of reverse map projection embeddings, each one defining a unique new method of encoding classical data into quantum states. Inspired by well-known map projections from the…
Invariant-based inverse engineering is an elegant approach to quantum control with corresponding experimental implementations that perform tasks with applications in quantum information processing such as shuttling trapped ions. We build on…
Quantum coherence allows for reduced-memory simulators of classical processes. Using recent results in single-shot quantum thermodynamics, we derive a minimal work cost rate for quantum simulators that is quasistatically attainable in the…