相关论文: Quantum Ballistic Evolution in Quantum Mechanics: …
Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent…
In optimal quantum-mechanical evolutions, motion can take place along paths of minimal length within an optimal time frame. Alternatively, optimal evolutions may occur along established paths without any waste of energy resources and…
Adiabatic limit is the presumption of the adiabatic geometric quantum computation and of the adiabatic quantum algorithm. But in reality, the variation speed of the Hamiltonian is finite. Here we develop a general formulation of adiabatic…
Quantum adiabatic evolution, an important fundamental concept inphysics, describes the dynamical evolution arbitrarily close to the instantaneous eigenstate of a slowly driven Hamiltonian. In most systems undergoing spontaneous…
Stochastic quantum trajectories, such as pure state evolutions under unitary dynamics and random measurements, offer a crucial ensemble description of many-body open system dynamics. Recent studies have highlighted that individual quantum…
Quantum computing has the potential to provide exponential performance benefits in processing over classical computing. It utilizes quantum mechanics phenomena (such as superposition, entanglement, and interference) to solve a computational…
In certain approaches to quantum computing the operations between qubits are non-deterministic and likely to fail. For example, a distributed quantum processor would achieve scalability by networking together many small components;…
In recent works we have used quantum tools in the analysis of the time evolution of several macroscopic systems. The main ingredient in our approach is the self-adjoint Hamiltonian $H$ of the system $\Sc$. This Hamiltonian quite often, and…
According to standard quantum theory, the time evolution operator of a quantum system is independent of the state of the system. One can, however, consider systems in which this is not the case: the evolution operator may depend on the…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
This paper extends work done to date on quantum computation by associating potentials with different types of computation steps. Quantum Turing machine Hamiltonians, generalized to include potentials, correspond to sums over tight binding…
We study the asymptotic position distribution of general quantum walks on a lattice, including walks with a random coin, which is chosen from step to step by a general Markov chain. In the unitary (i.e., non-random) case, we allow any…
Darwinian evolution requires (i) heritable records, (ii) repeatable copying with variation, and (iii) routine irreversibility. Categorical quantum mechanics (CQM) makes precise why ``copy'' and ``delete'' are not generic quantum operations:…
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is…
Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum…
Among the fundamental questions in computer science, at least two have a deep impact on mathematics. What can computation compute? How many steps does a computation require to solve an instance of the 3-SAT problem? Our work addresses the…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
Quantum computing is transitioning from laboratory research to industrial deployment, yet significant challenges persist: system scalability and performance, fabrication yields, and the advancement of algorithms and applications. We…
The construction of exactly-solvable models has recently been advanced by considering integrable $T\bar{T}$ deformations and related Hamiltonian deformations in quantum mechanics. We introduce a broader class of non-Hermitian Hamiltonian…
The success of adiabatic quantum computation (AQC) depends crucially on the ability to maintain the quantum computer in the ground state of the evolution Hamiltonian. The computation process has to be sufficiently slow as restricted by the…