Related papers: Can closed timelike curves or nonlinear quantum me…
Quantum computers show promise to solve select problems otherwise intractable on classical computers. However, noisy intermediate-scale quantum (NISQ) era devices are currently prone to various sources of error. Quantum error correction…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
In recent years, deep learning has had a profound impact on machine learning and artificial intelligence. At the same time, algorithms for quantum computers have been shown to efficiently solve some problems that are intractable on…
Two types of results are presented for distinguishing pure bipartite quantum states using Local Operations and Classical Communications. We examine sets of states that can be perfectly distinguished, in particular showing that any three…
We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat…
We argue that usual quantum statics and the dynamical equivalence of mixed quantum states to {\it probabilistic mixtures}suffice to guarantee a linear evolution law, which necessarily complies with the no-signaling condition. Alternatively,…
Nonlinear partial differential equations (PDEs) are crucial for modeling complex fluid dynamics and are foundational to many computational fluid dynamics (CFD) applications. However, solving these nonlinear PDEs is challenging due to the…
Digital-analog quantum computing (DAQC) is a universal computational paradigm that combines the evolution under an entangling Hamiltonian with the application of single-qubit gates. Since any unitary operation can be decomposed into a…
Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…
In a quantum computation with pure states, the generation of large amounts of entanglement is known to be necessary for a speedup with respect to classical computations. However, examples of quantum computations with mixed states are known,…
We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the…
Quantum simulation has begun to penetrate the field of quantum chemistry in hopes of efficiently calculating ground state energies and approximating real-time evolution. With modern research highlighting nonadiabatic dynamics, tunably…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
Quantum computers (QCs) must implement quantum error correcting codes (QECCs) to protect their logical qubits from errors, and modeling the effectiveness of QECCs on QCs is an important problem for evaluating the QC architecture. The…
In the geometry of quantum-mechanical processes, the time-varying curvature coefficient of a quantum evolution is specified by the magnitude squared of the covariant derivative of the tangent vector to the state vector. In particular, the…
In a recent paper, Mallett found a solution of the Einstein equations in which closed timelike curves (CTC's) are present in the empty space outside an infinitely long cylinder of light moving in circular paths around an axis. Here we show…
Continuous time crystals (CTCs) are characterized by sustained oscillations that break the time translation symmetry. Since the ruling out of equilibrium CTCs by no-go theorems, the emergence of such dynamical phases has been observed in…
Quantum computing (QC) offers a new computing paradigm that has the potential to provide significant speedups over classical computing. Each additional qubit doubles the size of the computational state space available to a quantum…
We investigate the capabilities of a quantum computer based on cold trapped ions in presence of non-dissipative decoherence. The latter is accounted by using the evolution time as a random variable and then averaging on a properly defined…
An enduring challenge in computer science is reducing the runtime required to solve computational problems. Quantum computing has attracted significant attention due to its potential to deliver asymptotically faster solutions to certain…