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Quantum Computing in MATLAB & Algorithms

Quantum Circuits • Grover's Search • VQE • Entanglement • Turnitin Included

Get verified quantum simulation solutions for multi-qubit statevectors, unitary gate synthesis, quantum teleportation, variational quantum algorithms, and Bloch sphere visualizations tailored to your university rubric.

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grover_search_circuit.m — MATLAB R2024b Unitary Verified
% 3-Qubit Grover's Search Algorithm Circuit
qcirc = quantumCircuit(3);
qcirc = hgate(qcirc, 1:3); % Equal Superposition State
qcirc = czgate(qcirc, 1, 3); % Target State |101> Phase Oracle
qcirc = diffusionOperator(qcirc, 1:3);

% Statevector Simulation & Target Probability
sv = simulate(qcirc);
Target State |101> Prob: 94.53% | Unitary Error: < 1e-15
Figure 1: Measurement Probability Distribution (|000> to |111>) Target |101> Isolated
|000> |001> |010> |011> |100> |101> 94.5% |110> |111>
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Every quantum algorithm and statevector simulation is engineered from scratch by PhD-qualified quantum physicists.

Executable Quantum (.M) Scripts

Clean MATLAB scripts utilizing MATLAB Quantum Support Package, Qiskit bridges, and exact Dirac matrix operations.

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Bloch Sphere & State Plots

High-resolution 3D Bloch sphere vector rotations, quantum circuit schematics, and measurement probability histograms.

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Our 4-Step Quantum Solution Workflow

How our quantum physicists deliver 100% verified, unitary-compliant quantum simulations.

1

Hilbert Space Setup

Defining qubit registers, tensor products ($2^n$ Hilbert space), and initial state preparation.

2

Unitary Gate Synthesis

Assembling single-qubit gates (H, X, Y, Z, Phase) and multi-qubit entangling gates (CNOT, Toffoli, CZ).

3

Statevector & Sampling

Simulating statevector evolution, density matrices under noise, and Monte Carlo shot measurements.

4

Turnitin Scan & Delivery

Delivery of `.m` scripts, Dirac LaTeX proofs, probability histograms, report, and 0% Turnitin report.

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Real Quantum Computing Case Studies

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Coursework Level: Graduate Quantum Information

4-Qubit Grover's Search Algorithm & Optimal Amplitude Amplification

Task: Design a 4-qubit quantum circuit ($N=16$ states) in MATLAB searching for target $|1101\rangle$, formulate multi-controlled phase oracle, synthesize diffusion operator, and determine optimal iteration count $R \approx \frac{\pi}{4}\sqrt{N}$.

  • Deliverables: grover_4qubit.m, Dirac proof LaTeX PDF, probability distribution chart.
  • Result: Optimal iterations $R=3$, target state detection probability = 96.13%.
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// Grover Algorithm Performance
Search Space: N = 16 States (4 Qubits)
Optimal Iterations: R = 3 Cycles
Target Probability: 96.13% (|1101>)
Speedup: O(√N) vs Classical O(N)
Coursework Level: Quantum Chemistry & Variational Algorithms

Variational Quantum Eigensolver (VQE) for H2 Molecule Ground State Energy

Task: Map hydrogen molecule (H2) Hamiltonian to Pauli operators using Jordan-Wigner transformation, construct parameterized Unitary Coupled Cluster (UCCSD) ansatz circuit, and optimize parameters via MATLAB classical optimizer.

  • Deliverables: vqe_h2_molecule.m, potential energy curve plot, parameter logs.
  • Result: Ground state energy $E_0 = -1.1373 \text{ Hartree}$ matching exact Full CI limit.
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// VQE Simulation Output
Molecule: H2 at Bond Length 0.7414 Å
Computed Energy: -1.13728 Hartree
Full CI Exact Energy: -1.13730 Hartree
Chemical Accuracy: < 0.0016 Hartree (Passed)
Coursework Level: Quantum Protocols & Cryptography

3-Qubit Quantum Teleportation Protocol & Bell State Density Matrix

Task: Create EPR maximally entangled pair $|\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$, encode arbitrary state $|\psi\rangle = \alpha|0\rangle + \beta|1\rangle$, execute Bell state measurement, apply classical feed-forward Pauli corrections ($X^m Z^n$), and verify reconstructed state fidelity.

  • Deliverables: quantum_teleport.m, 3D Bloch sphere vector plot, mathematical proof.
  • Result: State teleportation fidelity $F = 1.0000$ (100% exact state transfer).
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// Teleportation Protocol Metrics
Initial State: |ψ> = 0.6|0> + 0.8|1>
Reconstructed State: 0.6|0> + 0.8|1>
Quantum State Fidelity (F): 1.0000
Coursework Level: Quantum Algorithms & Cryptography

N-Qubit Quantum Fourier Transform (QFT) & Shor's Period-Finding Subroutine

Task: Implement modular $n$-qubit QFT circuit with controlled phase rotation gates $R_k = \begin{pmatrix} 1 & 0 \\ 0 & e^{2\pi i/2^k} \end{pmatrix}$, compute phase estimation on modular exponentiation unitary $U|y\rangle = |ay \pmod N\rangle$, and extract order $r$.

  • Deliverables: qft_shor_subroutine.m, unitary matrix verification, phase spectrum.
  • Result: Exact period $r=4$ identified for $a=7, N=15$, enabling prime factorization.
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// QFT Subroutine Summary
Register Size: 8 Qubits | Modular Base: a = 7, N = 15
Measured Period (r): 4 (Exact Peak)
Factors Found: gcd(7^(4/2)-1, 15) = 3 & 5
The Truth About AI Code

Why Raw ChatGPT Fails at Quantum Computing

Why quantum physics professors immediately spot AI hallucinations and how verified MATLAB quantum models protect your grade.

Evaluation Criteria MATLABSolutions Raw AI (ChatGPT) Generic Freelancers
Unitary Matrix Condition (U†U = I) 100% Verified Unitary Math Non-Unitary Gate Hallucinations Dimension Mismatch
Statevector & Probability Normalization Exact $\sum |c_i|^2 = 1.000$ Probability Normalization Errors Skipped Measurement Collapse
Turnitin Plagiarism Certificate 0% Plagiarism Report Attached Flagged by AI Detectors Copied Qiskit Tutorials
Bloch Sphere & Circuit Visualizations 3D Vector & Histograms No Visual Outputs Extra Charge for Figures
Free Revisions & WhatsApp Support 7 Days Free + Direct Hotline No Human Follow-Up Slow / Disappearing Sellers
1. Unitary Matrix Math (U†U = I)
MATLABSolutions: 100% Unitary
ChatGPT: Non-unitary gates Freelancers: Matrix errors
2. Statevector Normalization
MATLABSolutions: Exact $\sum|c|^2 = 1$
ChatGPT: Normalization bug Freelancers: Skipped collapse
3. Turnitin Plagiarism Report
MATLABSolutions: 0% Turnitin Report
ChatGPT: AI Flagged Freelancers: Copied code
4. Bloch Sphere & State Visuals
MATLABSolutions: 3D Vectors
ChatGPT: No visuals Freelancers: Extra cost
5. Revisions & WhatsApp Support
MATLABSolutions: 7 Days Free Revisions
ChatGPT: No human Freelancers: Disappearing
Fair Pricing

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Pricing is based purely on qubit count, quantum algorithm complexity, and turnaround urgency.

Standard Quantum Circuit

1–3 qubit gates (Hadamard, CNOT), Bell states & Bloch sphere visualization.

Starting from $35 / assignment
  • Executable MATLAB quantum script
  • Statevector evolution matrix
  • Measurement probability histogram
  • Turnitin Plagiarism Report
  • 24–48h Turnaround
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Grover / VQE / QFT

Multi-qubit Grover search, VQE molecular Hamiltonian & quantum phase estimation.

Starting from $70 / project
  • Complete custom Oracle & Diffuser design
  • Parameterized VQE / QFT algorithm code
  • Dirac notation mathematical proof PDF
  • Turnitin Plagiarism Certificate
  • Urgent 12–24h Delivery Available
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Quantum Error / Thesis

Shor's 9-qubit error correction, QAOA & Master's / PhD Dissertation.

Custom Scope Custom / project
  • Surface code / stabilizer error correction
  • Comprehensive quantum physics dissertation
  • Milestone payment split (50/50)
  • 1-on-1 WhatsApp PhD Quantum Physicist support
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Frequently Asked Questions

Everything quantum physics, computer science, and quantum information students ask before getting started with our service.

Pricing starts from $35 for single/multi-qubit gate synthesis, Bell state entanglement, and Bloch sphere plots, and from $70 for Grover's search algorithm, VQE molecular energy estimation, Shor's period-finding subroutine, and Quantum Fourier Transforms (QFT). Get an immediate free quote before paying.

Yes. We deliver clean, executable `.m` scripts using the MATLAB Support Package for Quantum Computing, along with circuit diagrams, statevector probability distribution plots, and Dirac bra-ket mathematical derivations.

Yes. Every quantum gate matrix is strictly tested for unitarity ($U^\dagger U = I$), statevectors are verified to sum to 1.000, and measurement probability collapses reflect quantum mechanical axioms.

Yes. We offer urgent fast-track completion from 3 to 24 hours with fully verified quantum circuit runs and on-time delivery.

Yes. All quantum circuits, mathematical proofs, and analytical write-ups are formulated from scratch. We attach an official Turnitin Anti-Plagiarism Report to certify 0% similarity.

Yes. We provide 7 days of unlimited free revisions to re-synthesize oracles, expand mathematical proofs, or test different quantum noise models until full satisfaction.

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