![]() In the right inset of (e), linear fits start at N q = 2 and 5 for M U = 1 and 4, respectively. (d)–(f) Same results for the g / J = h / J = 1 case. ![]() The horizontal dashed lines mark the theoretical maximum entanglement entropy levels ( N q − 1 ) log 2. Given an (unsorted) list L of (n) elements and a search key (K), we seek to identify one element in L which has key value (k), if any exists. (c) Entanglement entropy as a function of evolution time t J compared with the quasi-exact result. Given an array-based list implementation, deleting the current element takes how long in the average case. Linear Search is defined as a sequential search algorithm that starts at one end and goes through each element of a list until the desired element is found, otherwise the search continues till the end of the data set. The worst case for sequential search occurs when the last element of the array is the value being searched for. Right inset: The error in fidelity density 1 − F for different N q. The best case for the sequential search algorithm occurs when the array has only a single element. Left inset: The reachable time t * under the condition F ⩾ 1 − 10 − 4 as a function of N q. The blue markers show the results for l-USC, and the line shows the linear fit. Sequential search in C++ is also called a linear search. The black crosses represent the standard iTEBD approach with the black dashed line showing an exponential fit. (b) The number of parameters required to reach time t * with the fidelity density at least F = 1 − 10 − 4. Inset: The difference in the single-site density matrices between the quasi-exact iTEBD simulation and optimization of l-USC. (a) Expectation value of 〈 σ ̂ z ( t ) 〉 using l-USC with different values of N q. Simulations of time evolution using l-USC with M U = 1 and exact environment for the Hamiltonian in Eq. ( 8) with g / J = 1.0, h / J = 0 (upper row) and h / J = 1 with M U = 1 and 4 (lower row). If both are matched then result is element found otherwise. This search process starts comparing search element with the first element in the list. With more efficient tensor contraction schemes, this algorithm may also offer improvements as a classical numerical algorithm. Linear Search Algorithm (Sequential Search Algorithm) Linear search algorithm finds a given element in a list of elements with O(n) time complexity where n is total number of elements in the list. The basic algorithm is to find the middle element of the list, compare it against the key, decide which half of the list must contain the key, and repeat with. After benchmarking the evolution algorithm on a classical computer, we demonstrate the measurement of observables of this uniform state using a finite number of qubits on a cloud-based quantum processing unit. All steps of the hybrid optimization are designed with near-term digital quantum computers in mind. Furthermore, this favorable scaling of the Ansatz is maintained during our variational evolution algorithm. We show numerically that this Ansatz requires a number of parameters polynomial in the simulation time for a given accuracy. For searching, it makes sense to count the number of comparisons performed. Recall that this is typically the common step that must be repeated in order to solve the problem. This algorithm uses a layered uniform sequential quantum circuit as a variational Ansatz to represent infinite translation-invariant quantum states. To analyze searching algorithms, we need to decide on a basic unit of computation. In this work we present a polynomially scaling hybrid quantum-classical algorithm for time evolving a one-dimensional uniform system in the thermodynamic limit. I = 0 // intitial value for counter variable.Simulating time evolution of generic quantum many-body systems using classical numerical approaches has an exponentially growing cost either with evolution time or with the system size. Int arr = įlag = 0 // initial value for condition.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |