1. HNL Juniori stats & predictions

Why Choose Our Platform?

Our commitment to excellence is reflected in our comprehensive coverage of the Football 1. HNL Juniori Croatia. Here’s why our platform stands out:

• Real-Time Updates: Stay informed with live match updates that are refreshed daily, ensuring you never miss a moment of the action.
• Expert Predictions: Benefit from our team of seasoned analysts who provide accurate and insightful betting predictions.
• Detailed Analyses: Gain access to in-depth match analyses that cover team strategies, player performances, and historical data.
• User-Friendly Interface: Navigate our platform with ease, thanks to its intuitive design and seamless user experience.

Understanding Football 1. HNL Juniori Croatia

The Football 1. HNL Juniori Croatia is a premier youth league that showcases the future stars of Croatian football. It serves as a breeding ground for young talent, providing them with the opportunity to hone their skills and gain valuable match experience. The league is structured to promote competitive play while ensuring player development remains at the forefront.

The Structure of the League

The league is divided into several age groups, each competing in their respective divisions. This structure allows players to compete against peers of similar skill levels, fostering a healthy competitive environment. The focus is on developing well-rounded players who can excel both technically and tactically.

Key Teams and Players

Each season brings new talents to the forefront, but certain teams consistently produce standout players. Clubs like Dinamo Zagreb Youth Academy and Hajduk Split Youth Academy are renowned for their robust training programs and successful track records in nurturing future football stars.

• Dinamo Zagreb Youth Academy: Known for its rigorous training regimen and emphasis on tactical awareness.
• Hajduk Split Youth Academy: Celebrated for its focus on technical skills and creative playmaking.
• Rijeka Youth Academy: Recognized for producing resilient and physically strong players.

The Importance of Youth Leagues

Youth leagues like the Football 1. HNL Juniori Croatia play a crucial role in the football ecosystem. They provide a platform for young athletes to develop their skills in a competitive yet supportive environment. Moreover, these leagues contribute significantly to the national team's talent pool, ensuring a steady stream of capable players ready to represent Croatia on international stages.

Expert Betting Predictions: How We Do It

Betting on football can be both exciting and rewarding when approached with the right knowledge and tools. Our expert betting predictions are crafted using a combination of statistical analysis, historical data, and insider insights. Here’s how we ensure our predictions are top-notch:

Data-Driven Analysis

We utilize advanced algorithms and statistical models to analyze past performances, current form, head-to-head records, and other relevant metrics. This data-driven approach helps us identify patterns and trends that might not be immediately apparent.

Insider Insights

In addition to quantitative analysis, our experts bring qualitative insights from years of experience in football analytics. They consider factors such as team morale, recent injuries, and tactical changes that could impact match outcomes.

Comprehensive Match Reports

Each prediction is accompanied by a detailed match report that outlines key points to watch for during the game. These reports include player ratings, tactical formations, and potential game-changing moments.

• Tactical Formations: Understanding how teams set up on the pitch can provide clues about their game plan and potential weaknesses.
• Player Ratings: Assessing individual player performances helps gauge their impact on the match.
• Potential Game-Changers: Identifying moments or players that could tip the scales in favor of one team or another.

Betting Strategies

We also offer tailored betting strategies based on different risk appetites. Whether you prefer conservative bets or high-risk wagers, our experts provide guidance to help you make informed decisions.

• Cover Bets: A strategy that involves placing multiple bets across different outcomes to hedge against potential losses.
• Total Goals Bets: Focusing on predicting whether a match will have over or under a certain number of goals.
• In-Play Betting: Taking advantage of real-time odds fluctuations during the match for potentially higher returns.

Daily Match Updates: Stay Informed Every Day

To keep you updated with the latest developments in Football 1. HNL Juniori Croatia, we provide daily match updates. These updates cover everything from pre-match build-ups to post-match analyses, ensuring you have all the information you need at your fingertips.

Pre-Match Build-Up

Before each matchday, we offer insights into what to expect from upcoming fixtures. This includes team news, such as injuries or suspensions, as well as tactical previews highlighting key battles on the pitch.

• Injury Reports: Stay informed about which players are unavailable for selection due to injuries or suspensions.
• Tactical Previews: Learn about potential team line-ups and tactical approaches from both sides.

Live Match Updates

During matches, we provide live updates that capture all the critical moments as they happen. From goals and red cards to substitutions and tactical changes, our live coverage ensures you don’t miss a beat.

• Goal Alerts: Get notified instantly when goals are scored during matches.
• Injury Time Updates: Keep track of any additional time added at the end of each half.

Post-Match Analyses

After each matchday, we offer comprehensive post-match analyses that delve into what transpired during the games. These analyses include key takeaways, standout performances, and implications for future fixtures.

• Key Takeaways: Summarize the most important aspects of each matchday’s results.
• Standout Performances: Highlight players who made significant contributions during matches.

User Engagement Features

To enhance user engagement, our platform offers interactive features such as forums where fans can discuss matches and share their own predictions. Additionally, we host weekly polls where users can vote on their favorite players or predict match outcomes ahead of time.

• Fan Forums: Engage with other fans in discussions about recent matches or upcoming fixtures.

Meet Our Team of Experts

Behind every prediction lies a team of dedicated professionals who bring years of expertise in football analytics and betting strategies. Meet our experts who ensure you receive nothing but top-tier insights every day:

• Josip Horvat - Head Analyst: With over a decade of experience in sports analytics, Josip leads our team with his deep understanding of football tactics and statistical modeling techniques.
  
• Ana Petrović - Data Scientist: Ana specializes in developing predictive models using machine learning algorithms tailored specifically for football betting.
  
• Mario Jurić - Tactical Expert: Mario brings his extensive knowledge as an ex-professional coach to analyze formations and strategies employed by teams across all divisions.
  
• Elena Marković - Content Creator: Elena crafts engaging content that makes complex analyses accessible while keeping readers informed about every aspect related to Football1 HNL Juniori Croatia.
  
• Ivan Kovačić - Betting Strategist: Ivan’s expertise lies in formulating effective betting strategies based on current trends within Croatian youth leagues.
  kshirai/QuantumErrorCorrection<|file_sep|>/tomo.py #!/usr/bin/env python # -*- coding: utf-8 -*- # File: tomography.py # Author: Kai Sun import numpy as np import matplotlib.pyplot as plt from scipy.optimize import minimize from scipy.stats import unitary_group from qiskit import QuantumCircuit def get_state_tomography(qc): """ Return state tomography matrix. Args: qc (qiskit.QuantumCircuit): quantum circuit Returns: np.ndarray: state tomography matrix (d x d x m) m = number of measurement bases, d = dimension (for single qubit system m = d^2 =16) """ # get qubit number n_qubits = qc.num_qubits # get state tomography matrix U = np.zeros((2 ** n_qubits,) * (2 + n_qubits), dtype=complex) # iterate through all measurement bases for i_x in range(2 ** n_qubits): # create basis matrix (for single qubit system it's pauli matrices) basis_x = np.array([1 / np.sqrt(2) * np.array([[1., +1.j], [+1., +1.]]), np.array([[0., +1.j], [0., +0.]]), np.array([[1., +0], [0., -1]]), np.array([[+1.j], [-1]])]) # iterate through all measurement bases for i_y in range(2 ** n_qubits): # create basis matrix (for single qubit system it's pauli matrices) basis_y = np.array([np.array([[1 / np.sqrt(2), +1 / np.sqrt(2)]], [[+1 / np.sqrt(2), -1 / np.sqrt(2)]]), np.array([[0., +1], [0., +0]]), np.array([[1., +0], [-1., +0]]), np.array([[+1.j], [-1.j]])]) # create circuit copy qc_tomo = qc.copy(name=f'tomography_{i_x}_{i_y}') # add measurement gates for j_qubit in range(n_qubits): if ((i_x >> j_qubit) & (0x01)) == (0x01): qc_tomo.u3(np.pi / -2., np.pi / -2., np.pi / -2., j_qubit) if ((i_y >> j_qubit) & (0x01)) == (0x01): qc_tomo.u3(np.pi / -2., np.pi / -2., np.pi, j_qubit) qc_tomo.measure(j_qubit, j_qubit) # measure j-th qubit job_tomo = execute(qc_tomo, backend=backend, shots=1024, memory=True) result_tomo = job_tomo.result() counts_tomo = result_tomo.get_counts(qc_tomo) prob_vec = [] # iterate through all possible states (for single qubit system it's |00>, |01>, ...) for i_z in range(2 ** n_qubits): if counts_tomo.get(bin(i_z)[2:].zfill(n_qubits), None) != None: prob_vec.append(counts_tomo[bin(i_z)[2:].zfill(n_qubits)]) else: prob_vec.append(0) # calculate probability vector prob_vec = np.array(prob_vec) / sum(prob_vec) U[i_x][i_y] = prob_vec.reshape(2 ** n_qubits) # calculate outer product between two basis matrices U[i_x] = basis_x[i_x].dot(basis_y[i_y].conj().T) return U def get_process_tomography(qc): """ Return process tomography matrix. Args: qc (qiskit.QuantumCircuit): quantum circuit Returns: np.ndarray: process tomography matrix (d x d x m x n) m,n = number of measurement bases, d = dimension (for single qubit system m,n=d^2=16) dim(U) should be equal to d x d x m x n. The last two dimensions should be square matrices. dim(U)[0] is assumed as input basis vector index. dim(U)[1] is assumed as output basis vector index. dim(U)[2] is assumed as input measurement basis index. dim(U)[3] is assumed as output measurement basis index. """ # get qubit number n_qubits = qc.num_qubits # get process tomography matrix U = np.zeros((2 ** n_qubits,) * (3 + n_qubits), dtype=complex) # iterate through all measurement bases for i_z in range(2 ** n_qubits): # create circuit copy qc_prep = QuantumCircuit(n_qubits) if ((i_z >> (n_qubits - n_ancilla)) & (0x01)) == (0x01): qc_prep.x(n_ancilla) if ((i_z >> (n_ancilla - n_data)) & (0x01)) == (0x01): qc_prep.x(n_data) # add initial gate preparation circuit qc_prep.compose(qc.data[:(n_data * len(gateset) + len(gateset))], inplace=True) U_prep = get_state_tomography(qc_prep) # iterate through all measurement bases for i_x in range(2 ** n_qubits): # create basis matrix (for single qubit system it's pauli matrices) basis_x = np.array([np.array([[1 / np.sqrt(2), +1 / np.sqrt(2)]], [[+1 / np.sqrt(2), -1 / np.sqrt(2)]]), np.array([[0., +1], [0., +0]]), np.array([[1., +0], [-1., +0]]), np.array([[+1.j], [-1.j]])]) # iterate through all measurement bases for i_y in range(2 ** n_qubits): # create circuit copy qc_meas = QuantumCircuit(n_ancilla) if ((i_y >> (n_ancilla - n_data)) & (0x01)) == (0x01): qc_meas.x(n_data) if ((i_z >> (n_ancilla - n_data)) & (0x01)) == (0x01): qc_meas.x(n_data) qc_meas.compose(qc.data[n_data * len(gateset) + len(gateset):], inplace=True) U_meas = get_state_tomography(qc_meas) U[i_x][i_y][i_z] = U_meas[i_x][i_y].dot( U_prep[i_x][i_y].conj().T) U[i_x][i_y][i_z] /= trace( U[i_x][i_y][i_z]) # normalize trace U[i_x][i_y][i_z] *= basis_x[i_x].dot(basis_x[i_y].conj().T) return U def reconstruct_state(U): """ Reconstruct density matrix from state tomography data. Args: U (np.ndarray): state tomography matrix returned by get_state_tomography() dim(U)[dim(U)-n-qubits]: number of measurement bases, dim(U)[dim(U)-n-qubits-1]: dimension, dim(U)[dim(U)-n-qubits-2]: input state index, dim(U)[dim(U)-n-qubits-3]: output state index. For single qubit system m=d^2=16. dim(U)[dim(U)-n-qubits-3] should be equal to m. dim(U)[dim(U)-n-qubits-4] should be equal to d. dim(U)[dim(U)-n-qubits-5] should be equal to d. dim(U)[dim(U)-n-qubits-6:] should be equal to identity matrix. dim(U)[dim(U)-n-qubits-6:] should be square matrices. For example: dim(state_U)=16x16x16x16, state_U[:, :, :, :] gives density matrix elements rho_ij. state_U[:, :, :, k] gives rho_ij when input state is k-th state. Note that dimension(d) depends on your system. For example: d=16 when there are two qubits. d=8 when there is one qudit with four levels. For general case: d=local_dimension**num_qudits where local_dimension means number levels per qudit. For example: For two qutrits local_dimension=3 so d=9. For three qutrits local_dimension=3 so d=27