相关论文: Complexity for one-dimensional discrete time quant…

Given a unitary transformation, what is the size of the smallest quantum circuit that implements it? This quantity, known as the quantum circuit complexity, is a fundamental property of quantum evolutions that has widespread applications in…

Existing quantum discrete adiabatic approaches are hindered by circuit depth that increases linearly with the number of evolution steps, a significant challenge for current quantum hardware with limited coherence times. To address this, we…

We establish a direct connection between spread complexity and quantum circuit complexity by demonstrating that spread complexity emerges as a limiting case of a circuit complexity framework built from two fundamental operations:…

Noise-enhanced applications in open quantum walk (QW) have recently seen a surge due to their ability to improve performance. However, verifying the success of open QW is challenging, as mixed-state tomography is a resource-intensive…

In this paper, we study mixing and large decoherence in continuous-time quantum walks on one dimensional regular networks, which are constructed by connecting each node to its $2l$ nearest neighbors($l$ on either side). In our…

Open Quantum Walks (OQW) are a type of quantum walk governed by the system's interaction with its environment. We explore the time evolution and the limit behavior of the OQW framework for Quantum Computation and show how we can represent…

For chaotic quantum dynamics modeled by random unitary circuits, we study the complexity of reduced density matrices of subsystems as a function of evolution time where the initial global state is a product pure state. The state complexity…

Discrete-time quantum walks (DTQWs) in random artificial electric and gravitational fields are studied analytically and numerically. The analytical computations are carried by a new method which allows a direct exact analytical…

Estimation of the coin parameter(s) is an important part of the problem of implementing more robust schemes for quantum simulation using quantum walks. We present the estimation of the quantum coin parameter used for one-dimensional…

We describe a method to simulate Hamiltonian evolution on a quantum computer by repeatedly using a superposition of steps of a quantum walk, then applying a correction to the weightings for the numbers of steps of the quantum walk. This…

We consider unitary dynamical evolutions on n qubits caused by time dependent pair-interaction Hamiltonians and show that the running time of a parallelized two-qubit gate network simulating the evolution is given by the time integral over…

We develop qutrit circuit models for discrete-time three-state quantum walks on Cayley graphs corresponding to Dihedral groups $D_N$ and the additive groups of integers modulo any positive integer $N$. The proposed circuits comprise of…

We derive the continuous spacetime limit of the one dimensional lazy discrete time quantum walk, obtaining explicit macroscopic evolution equations for a three state model in the presence of decoherence. While continuum limits of two state…

We calculate Nielsen's circuit complexity of coherent spin state operators. An expression for the complexity is obtained by using the small angle approximation of the Euler angle parametrisation of a general $SO(3)$ rotation. This is then…

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…

We consider circuit complexity in certain interacting scalar quantum field theories, mainly focusing on the $\phi^4$ theory. We work out the circuit complexity for evolving from a nearly Gaussian unentangled reference state to the entangled…

We consider the effect of different unitary noise mechanisms on the evolution of a quantum walk (QW) on a linear chain with a generic coin operation: (i) bit-flip channel noise, restricted to the coin subspace of the QW, and (ii)…

We present an extension to the quantum walk search framework that facilitates quantum walks with nested updates. We apply it to give a quantum walk algorithm for 3-Distinctness with query complexity ~O(n^{5/7}), matching the best known…

We implement the discrete-time quantum walk model using the continuous-time evolution of the Hamiltonian that includes both the shift and the coin generators. Based on the Trotter-Suzuki first-order approximation, we consider an…

The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining…