Related papers: Quantum Simulation of Markov Chains
Computer simulation of observable phenomena is an indispensable tool for engineering new technology, understanding the natural world, and studying human society. Yet the most interesting systems are often complex, such that simulating their…
Non-Markovian quantum processes exhibit different memory effects when measured in different ways; an unambiguous characterization of memory length requires accounting for the sequence of instruments applied to probe the system dynamics.…
Models for open quantum systems, which play important roles in electron transport problems and quantum computing, must take into account the interaction of the quantum system with the surrounding environment. Although such models can be…
Quantum simulators are controllable systems that can be used to simulate other quantum systems. Here we focus on the dynamics of a chain of molecular qubits with interposed antiferromagnetic dimers. We theoretically show that its dynamics…
Quantum algorithms present a quadratically improved complexity over classical ones for certain sampling tasks. For instance, the Quantum Amplitude Estimation (QAE) algorithm promises to speedup the estimation of the mean of certain…
Increasingly sophisticated programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large…
We study the real-time simulation of open quantum systems, where the system is modeled by a spin chain, with each spin associated with its own harmonic bath. Our method couples the inchworm method for the spin-boson model and the modular…
Quantum algorithms can potentially solve a handful of problems more efficiently than their classical counterparts. In that context, it has been discussed that Markov chains problems could be solved significantly faster using quantum…
In this work, we consider a probability representation of quantum dynamics for finite-dimensional quantum systems with the use of pseudostochastic maps acting on true probability distributions. These probability distributions are obtained…
We propose that neuromorphic computing can perform quantum operations. Spiking neurons in the active or silent states are connected to the two states of Ising spins. A quantum density matrix is constructed from the expectation values and…
We present an approach to the simulation of quantum systems driven by classical stochastic processes that is based on the polynomial chaos expansion, a well-known technique in the field of uncertainty quantification. The polynomial chaos…
Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living…
This article is a tutorial on Markov chain Monte Carlo simulations and their statistical analysis. The theoretical concepts are illustrated through many numerical assignments from the author's book on the subject. Computer code (in Fortran)…
A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…
So far proposed quantum computers use fragile and environmentally sensitive natural quantum systems. Here we explore the new notion that synthetic quantum systems suitable for quantum computation may be fabricated from smart nanostructures…
Quantum metrology based on quantum entanglement and quantum coherence improves the accuracy of measurement. In this paper, we briefly review the schemes of quantum metrology in various complex systems, including non-Markovian noise,…
Quantum trajectories are Markov chains modeling quantum systems subjected to repeated indirect measurements. Their stationary regime depends on what observables are measured on the probes used to indirectly measure the system. In this…
In statistical modeling of computer experiments sometimes prior information is available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all…
Numerical simulation is an important method for verifying the quantum circuits used to simulate low-energy nuclear states. However, real-world applications of quantum computing for nuclear theory often generate deep quantum circuits that…
The classical embeddability problem asks whether a given stochastic matrix $T$, describing transition probabilities of a $d$-level system, can arise from the underlying homogeneous continuous-time Markov process. Here, we investigate the…