Characterizing errors for Quantum Fourier Transform on IBM Q

Abstract

The performance of today's quantum computers are affected by noise. This effect can be analyzed in the result of simple quantum algorithms in real quantum computers. The noise can be characterized as a decoherence error or a systematic error, the last could be corrected by a unitary rotation. In this article we propose two methods to model a systematic error, in the Quantum Fourier Transform algorithm (QFT). The first method uses the isotropic index presented in `` [1] and needs to reconstruct the density matrix of the experimental state, while the second method, although less general, only needs to reconstruct the reduced density matrices for each qubit. In both methods, a unitary transformation is proposed, which approximates the experimental result to the expected theoretical state. As an example, the QFT algorithm is analyzed for two qubit states, in quantum IBM Q computer ibmq\_santiago.

Quantum AI and hybrid simulators for a Universal Quantum Field Computation Model

“…This section reviews selected QFCMs listed in Table 1 . QFCMs simulating QFThs [2 , 18] and QFTs [7 , 12 , 23] , are compared to the QDF model [7] , [8] , [9] , [10] . This model selection is made on the basis of model limitations e.g., uncertainties [17 , [26] , [27] , [28] , error rates and strengths as (see, Section 2), for projecting reliable predictions of the final system state, Eq.…”

“…2], by using quantum computational methods to simulate thermodynamic systems and events [7] , [8] , [9] , [10] , [11] , [12] , 23] . Among which are systems in condensed matter physics, e.g., BEC [25] , in HEP, e.g., the Hadron Collider (LHC) [13 , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , 48] , in chemistry and nuclear physics, NMR [16] . To predict new matter forms and system states, the system’s PT or ST is simulated and observed on quantum and classical scales.…”

“…1 displays an imaginary plot projection on such predictive models in some areas of science and technology, including experiments conducted on QFThs, such as LHC, and laser interferometer gravitational-wave observatory (LIGO). The plot shows where in-demand devices for users require greater performance in processing massive amounts of data available on the internet and media, such as Google and IBM [12 , 15 , [22] , [23] , [24] . Nowadays, devices are hybridized between the quantum mechanical and classical computation models [18 , 43 , 44] , as discussed earlier (or see Graphical Abstract, step 5).…”

“…In [22] , [23] , [24] , IBM-QE devices were used to code and simulate QFTh and QFTs in their proposed methods. The focus of these studies was on simulating condensed matter, spin Hamiltonian, potential wells, quantum circuits, and thermodynamic system models.…”

“…Earlier QFCMs discussed for [3] , [4] , [5] , [6] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , collectively satisfy (1) , (2) , (3) , (4) , (5) , but not on doubling the values of the ST probability space and its correlation to the system’s pending ST or PT. The combination of model strengths, e.g., implementing a maximum fidelity strategy on performing a QDF transform with models [12 , 16] , can achieve a UQFCM with high ’s in predicting strong ’s for a system.…”