相关论文: A polynomial-time dissipation-based quantum algori…
The famous, yet unsolved, Fermi-Hubbard model for strongly-correlated electronic systems is a prominent target for quantum computers. However, accurately representing the Fermi-Hubbard ground state for large instances may be beyond the…
We consider finite-dimensional Markovian open quantum systems, and characterize the extent to which time-independent Hamiltonian control may allow to stabilize a target quantum state or subspace and optimize the resulting convergence speed.…
Computing vacuum states of lattice gauge theories (LGTs) containing fermionic degrees of freedom can present significant challenges for classical computation using Monte-Carlo methods. Quantum algorithms may offer a pathway towards more…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
Advancements in the implementation of quantum hardware have enabled the acquisition of data that are intractable for emulation with classical computers. The integration of classical machine learning (ML) algorithms with these data holds…
In open quantum systems, the Liouvillian gap characterizes the relaxation time toward the steady state. However, accurately computing this quantity is notoriously difficult due to the exponential growth of the Hilbert space and the…
The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…
Discrete and continuous variables oftentimes require different treatments in many learning tasks. Identifying the Hamiltonian governing the evolution of a quantum system is a fundamental task in quantum learning theory. While previous works…
Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…
Gradient descent is a fundamental algorithm in both theory and practice for continuous optimization. Identifying its quantum counterpart would be appealing to both theoretical and practical quantum applications. A conventional approach to…
One of the central challenges in the study of quantum many-body systems is the complexity of simulating them on a classical computer. A recent advance of Landau et al. gave a polynomial time algorithm to actually compute a succinct…
Quantum algorithms exploiting real-time evolution under a target Hamiltonian have demonstrated remarkable efficiency in extracting key spectral information. However, the broader potential of these methods, particularly beyond ground state…
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum)…
We study the problem of learning a local quantum Hamiltonian $H$ given copies of its Gibbs state $\rho = e^{-\beta H}/\textrm{tr}(e^{-\beta H})$ at a known inverse temperature $\beta>0$. Anshu, Arunachalam, Kuwahara, and Soleimanifar…
Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work we consider time-periodically modulated quantum systems which are in contact with a stationary…
Many nonlinear PDEs have singular or oscillatory solutions or may exhibit physical instabilities or uncertainties. This requires a suitable concept of physically relevant generalized solutions. Dissipative measure-valued solutions have been…
We present a general variational approach to determine the steady state of open quantum lattice systems via a neural network approach. The steady-state density matrix of the lattice system is constructed via a purified neural network ansatz…
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…
Understanding and characterising quantum many-body dynamics remains a significant challenge due to both the exponential complexity required to represent quantum many-body Hamiltonians, and the need to accurately track states in time under…
Simulation of realistic classical mechanical systems is of great importance to many areas of engineering such as robotics, dynamics of rotating machinery and control theory. In this work, we develop quantum algorithms to estimate quantities…