Related papers: Realizing Unitary $k$-designs with a Single Quench
We study spectral properties and the dynamics after a quench of one-dimensional spinless fermions with short-range interactions and long-range random hopping. We show that a sufficiently fast decay of the hopping term promotes localization…
Randomness, mainly in the form of random numbers, is the fundamental prerequisite for the security of many cryptographic tasks. Quantum randomness can be extracted even if adversaries are fully aware of the protocol and even control the…
We demonstrate the advantages of randomization in coherent quantum dynamical control. For systems which are either time-varying or require decoupling cycles involving a large number of operations, we find that simple randomized protocols…
We show that every finite-dimensional quantum system with Markovian (i.e., GKLS-generated) time evolution has an autonomous unitary dilation which can be dynamically decoupled. Since there is also always an autonomous unitary dilation which…
We revisit the problem of switching off unwanted phase evolution and decoherence in a single two-state quantum system in the light of recent results on random dynamical decoupling methods [L. Viola and E. Knill, Phys. Rev. Lett. {\bf 94},…
The unitary generation of coherence from an incoherent thermal state is investigated. We consider a completely controllable Hamiltonian allowing to generate all possible unitary transformations. Optimizing the unitary control to achieve…
As established in the seminal work by Berry et al.[1], expanding the time evolution operator using truncated Taylor series (up to some order $K$) makes a good candidate for simulating Hamiltonian dynamics. Here, we adapt the method but…
We derive an upper bound for the time needed to implement a generic unitary transformation in a $d$ dimensional quantum system using $d$ control fields. We show that given the ability to control the diagonal elements of the Hamiltonian,…
Quantum computation and quantum control operate by building unitary transformations out of sequences of elementary quantum logic operations or applications of control fields. This paper puts upper bounds on the minimum time required to…
Quantum generative modeling, where the Born rule naturally defines probability distributions through measurement of parameterized quantum states, is a promising near-term application of quantum computing. We propose a Quantum Scrambling…
Inspired by the Hayden-Preskill protocol for black hole evaporation, we consider the dynamics of a quantum many-body qudit system coupled to an external environment, where the time evolution is driven by the continuous limit of certain…
We investigate the quench of half-filled 1D and 2D fermionic Hubbard models to models without Coulomb interaction. Since the time propagation is gaussian we can use a variety of time-dependent quantum Monte Carlo methods to tackle this…
We show that the discrete-time evolution of an open quantum system generated by a single quantum channel $T$ can be embedded in the discrete-time evolution of an enlarged closed quantum system, i.e. we construct a unitary dilation of the…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…
Renormalization-group methods provide a viable approach for investigating the emergent collective behavior of classical and quantum statistical systems in both equilibrium and nonequilibrium conditions. Within this approach we investigate…
Quantum and random walks have been shown to be equivalent in the following sense: a time-dependent random walk can be constructed such that its vertex distribution at all time instants is identical to the vertex distribution of any…
Given a universal gate set on two qubits, it is well known that applying random gates from the set to random pairs of qubits will eventually yield an approximately Haar-distributed unitary. However, this requires exponential time. We show…
The evolution of a quantum system interacting with an environment can be described as a unitary process acting on both the system and the environment. In this framework, the system's evolution can be predicted by tracing out the…
Entangled photons are widely used in quantum technologies. Many photonic experiments generate them with probabilistic photon-pair sources that can be modeled as squeeze operators. In practice, these sources are usually treated in the…
We consider random quantum circuits (RQC) on arbitrary connected graphs whose edges determine the allowed $2$-qudit interactions. Prior work has established that such $n$-qudit circuits with local dimension $q$ on 1D, complete, and…