Related papers: Digital Quantum Simulation of Reaction-Diffusion S…
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…
The dramatic increase in the efficiency of a quantum computer over a classical computer, raises a natural question asking, how much of this success could be attributed to its quantum nature and how much to its probabilistic content. To…
This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena,…
The quest for improved sampling methods to solve statistical mechanics problems of physical and chemical interest proceeds with renewed efforts since the invention of the Metropolis algorithm, in 1953. In particular, the understanding of…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
Numerical simulation of turbulent fluid dynamics needs to either parameterize turbulence-which introduces large uncertainties-or explicitly resolve the smallest scales-which is prohibitively expensive. Here we provide evidence through…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
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…
Quantum simulations of strongly interacting fermionic systems, such as those described by the Hubbard model, are promising candidates for useful early fault-tolerant quantum computing applications. This paper presents Tile Trotterization, a…
The simulation of dense fermionic matters is a long-standing problem in lattice gauge theory. One hopeful solution would be the use of quantum computers. In this paper, digital quantum simulation is designed for lattice gauge theory at…
When simulating the dynamics of open quantum systems with quantum computers, it is essential to accurately approximate the system's behaviour while preserving the physicality of its evolution. Traditionally, for Markovian open quantum…
Imaginary time evolution is a powerful tool for studying quantum systems. While it is possible to simulate with a classical computer, the time and memory requirements generally scale exponentially with the system size. Conversely, quantum…
We review and extend, in a self-contained way, the mathematical foundations of numerical simulation methods that are based on the use of random states. The power and versatility of this simulation technology is illustrated by calculations…
Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays traveling waves in its…
Quantum simulators are attracting great interest because they promise insight into the behavior of quantum many-body systems that are prohibitive for classical simulations. The generic output of quantum simulators are snapshots, obtained by…
Digital quantum computers have the potential to simulate complex quantum systems. The spin-boson model is one of such systems, used in disparate physical domains. Importantly, in a number of setups, the spin-boson model is open, i.e. the…
Spin-1 systems, in comparison to spin-1/2 systems, offer a better security for encoding and transfer of quantum information, primarily due to their larger Hilbert spaces. Superconducting artificial atoms possess multiple energy-levels,…
We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar…
High-dimensional fractional reaction-diffusion equations have numerous applications in the fields of biology, chemistry, and physics, and exhibit a range of rich phenomena. While classical algorithms have an exponential complexity in the…
Quantum simulation is a promising pathway toward practical quantum advantage by simulating large-scale quantum systems. In this work, we propose communication-efficient distributed quantum simulation protocols by exploring three quantum…