Related papers: Universal Early-Time Growth in Quantum Circuit Com…
Evolution time of a qubit under a Hamiltonian operation is one of the key issues in quantum control, quantum information processing and quantum computing. It has a lower bound in Hermitian system, which is limited by the coupling between…
In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive…
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…
Real-time evolution of quantum field theories using classical computers requires resources that scale exponentially with the number of lattice sites. Because of a fundamentally different computational strategy, quantum computers can in…
Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace…
We develop a fourth-order Magnus expansion based quantum algorithm for the simulation of many-body problems involving two-level quantum systems with time-dependent Hamiltonians, $\mathcal{H}(t)$. A major hurdle in the utilization of the…
Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure…
Proofs are given that the quantum-mechanical description of the LC-circuit with a time dependent external source can be readily established by starting from a general discretization rule of the electric charge. For this purpose one resorts…
For quantum theories with a classical limit (which includes the large N limits of typical field theories), we derive a hierarchy of evolution equations for equal time correlators which systematically incorporate corrections to the limiting…
We construct a time-dependent expression of the computational complexity of a quantum system which consists of two conformal complex scalar field theories in d dimensions coupled to constant electric potentials and defined on the boundaries…
We present a quantum algorithm for simulating the time evolution generated by any bounded, time-dependent operator $-A$ with non-positive logarithmic norm, thereby serving as a natural generalization of the Hamiltonian simulation problem.…
Unitary operations are the building blocks of quantum programs. Our task is to design effcient or optimal implementations of these unitary operations by employing the intrinsic physical resources of a given n-qubit system. The most common…
Attempts to consider evolution across space-time singularities often lead to quantum systems with time-dependent Hamiltonians developing an isolated singularity as a function of time. Examples include matrix theory in certain singular…
In this work, we decompose the time-evolution of the Bose-Hubbard model into a sequence of logic gates that can be implemented on a continuous-variable photonic quantum computer. We examine the structure of the circuit that represents this…
We consider $d$-dimensional quantum systems which for positive times evolve with a time-independent Hamiltonian in a nonequilibrium state that we keep generic in order to account for arbitrary evolution at negative times. We show how the…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points. A choice among these…
The simulation of quantum dynamics calls for quantum algorithms working in first quantized grid encodings. Here, we propose a variational quantum algorithm for performing quantum dynamics in first quantization. In addition to the usual…
We continue the study of time-dependent Hamiltonians with an isolated singularity in their time dependence, describing propagation on singular space-times. In previous work, two of us have proposed a "minimal subtraction" prescription for…
Notions of circuit complexity and cost play a key role in quantum computing and simulation where they capture the (weighted) minimal number of gates that is required to implement a unitary. Similar notions also become increasingly prominent…
In the context of Effective Field Theory, the Hilbert space of states increases in an expanding universe. Hence, the time evolution cannot be unitary. The formation of structure is usually studied using effective field theory techniques. We…