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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 Physics · Physics 2024-09-04 John M. Martyn , Yuan Liu , Zachary E. Chin , Isaac L. Chuang

We consider quantum computational models defined via a Lie-algebraic theory. In these models, specified initial states are acted on by Lie-algebraic quantum gates and the expectation values of Lie algebra elements are measured at the end.…

Quantum Physics · Physics 2009-11-13 Rolando Somma , Howard Barnum , Gerardo Ortiz , Emanuel Knill

To gain deeper insight into the dynamics of complex quantum systems we need a quantum leap in computer simulations. We can not translate quantum behaviour arising with superposition states or entanglement efficiently into the classical…

Quantum Physics · Physics 2008-02-28 Axel Friedenauer , Hector Schmitz , Jan Tibor Glückert , Diego Porras , Tobias Schätz

The quantum approximate optimization algorithm (QAOA) applies two Hamiltonians to a quantum system in alternation. The original goal of the algorithm was to drive the system close to the ground state of one of the Hamiltonians. This paper…

Quantum Physics · Physics 2018-12-31 Seth Lloyd

We introduce a quantum information theory-inspired method to improve the characterization of many-body Hamiltonians on near-term quantum devices. We design a new class of similarity transformations that, when applied as a preprocessing…

Quantum Physics · Physics 2024-07-24 Andi Gu , Hong-Ye Hu , Di Luo , Taylor L. Patti , Nicholas C. Rubin , Susanne F. Yelin

Accurate modeling of driven light-matter interactions is essential for quantum technologies, where natural and synthetic atoms are used to store and process quantum information, mediate interactions between bosonic modes, and enable…

Quantum Physics · Physics 2025-09-04 Martin Jirlow , Kunal Helambe , Axel M. Eriksson , Simone Gasparinetti , Tahereh Abad

The partition function and free energy of a quantum many-body system determine its physical properties in thermal equilibrium. Here we study the computational complexity of approximating these quantities for $n$-qubit local Hamiltonians.…

Quantum Physics · Physics 2023-09-22 Sergey Bravyi , Anirban Chowdhury , David Gosset , Pawel Wocjan

The simulation of quantum systems is a task for which quantum computers are believed to give an exponential speedup as compared to classical ones. While ground states of one-dimensional systems can be efficiently approximated using Matrix…

Quantum Physics · Physics 2009-11-13 Norbert Schuch , Michael M. Wolf , Karl Gerd H. Vollbrecht , J. Ignacio Cirac

Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, $PT$ symmetry, and resonances. However, the quantum simulation of these models has been limited by the…

Quantum Physics · Physics 2025-02-20 Anastashia Jebraeilli , Michael R. Geller

After a brief survey of the definition and the properties of Lambda-symmetries in the general context of dynamical systems, the notion of "Lambda-constant of motion'' for Hamiltonian equations is introduced. If the Hamiltonian problem is…

Mathematical Physics · Physics 2011-02-17 Giampaolo Cicogna

This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To…

Quantum Physics · Physics 2009-11-13 Daniel F. V. James , Jonathan Jerke

We consider quantum dynamics of systems with fast spatial modulation of the Hamiltonian. Employing the formalism of supersymmetric quantum mechanics and decoupling fast and slow spatial oscillations we demonstrate that the effective…

Quantum Physics · Physics 2019-04-10 Viktor Novičenko , Julius Ruseckas , Egidijus Anisimovas

In the field of quantum control, effective Hamiltonian engineering is a powerful tool that utilises perturbation theory to mitigate or enhance the effect that a variation in the Hamiltonian has on the evolution of the system. Here, we…

Quantum Physics · Physics 2020-09-11 Holger Haas , Daniel Puzzuoli , Feihao Zhang , David G. Cory

According to a fundamental result in quantum computing, any unitary transformation on a composite system can be generated using so-called 2-local unitaries that act only on two subsystems. Beyond its importance in quantum computing, this…

Quantum Physics · Physics 2024-08-15 Iman Marvian

Quantum signal processing provides an optimal procedure for simulating Hamiltonian evolution on a quantum computer using calls to a block encoding of the Hamiltonian. In many situations it is possible to control between forward and reverse…

Quantum Physics · Physics 2024-07-17 Dominic W. Berry , Danial Motlagh , Giacomo Pantaleoni , Nathan Wiebe

Analog quantum simulators with global control fields have emerged as powerful platforms for exploring complex quantum phenomena. Despite these advances, a fundamental theoretical question remains unresolved: to what extent can such systems…

We present a hybrid quantum-classical algorithm to simulate thermal states of a classical Hamiltonians on a quantum computer. Our scheme employs a sequence of locally controlled rotations, building up the desired state by adding qubits one…

Quantum Physics · Physics 2015-03-17 Man-Hong Yung , Daniel Nagaj , James D. Whitfield , Alán Aspuru-Guzik

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…

Quantum Physics · Physics 2014-10-17 B. E. Anderson , H. Sosa-Martinez , C. A. Riofrío , I. H. Deutsch , P. S. Jessen

We elaborate the idea of quantum computation through measuring the correlation of a gapped ground state, while the bulk Hamiltonian is utilized to stabilize the resource. A simple computational primitive, by pulling out a single spin…

Quantum Physics · Physics 2010-07-29 Akimasa Miyake

We study the Hamiltonian-independent contribution to the complexity of quantum optimal control problems. The optimization of controls that steer quantum systems to desired objectives can itself be considered a classical dynamical system…

Quantum Physics · Physics 2007-08-28 Raj Chakrabarti , Rebing Wu , Herschel Rabitz