Variational Quantum Eigensolver (VQE) Algorithm Implementation
VQE is a quantum-classical hybrid algorithm for finding the ground state energy of quantum systems. It uses a parameterized quantum circuit (ansatz) to prepare trial states and classical optimization to minimize the energy expectation value.
Key Features:
Algorithm Flow:
This implementation targets production use with real quantum hardware.
Variational Quantum Eigensolver (VQE) Algorithm Implementation
VQE is a quantum-classical hybrid algorithm for finding the ground state energy
of quantum systems. It uses a parameterized quantum circuit (ansatz) to prepare
trial states and classical optimization to minimize the energy expectation value.
Key Features:
- Multiple ansatz types (hardware-efficient, UCCSD-inspired, symmetry-preserving)
- Pau ;; Fallback to standard optimization without convergence monitoring for non-enhanced objectives
(va/run-variational-optimization objective-fn initial-parameters options)))) ;; Fallback to standard optimization without convergence monitoring for non-enhanced objectives
(va/run-variational-optimization objective-fn initial-parameters options)))) string Hamiltonian representation with measurement grouping
- Integration with fastmath optimization for classical optimization
- Comprehensive analysis and convergence monitoring
- Support for both gate-based and measurement-based implementations
Algorithm Flow:
1. Initialize parameterized quantum circuit (ansatz)
2. Prepare trial state |ψ(θ)⟩ with parameters θ
3. Measure expectation value ⟨ψ(θ)|H|ψ(θ)⟩
4. Use classical optimizer to update parameters
5. Repeat until convergence
This implementation targets production use with real quantum hardware.(heisenberg-hamiltonian num-sites)(heisenberg-hamiltonian num-sites coupling)(heisenberg-hamiltonian num-sites coupling periodic)Create a Heisenberg model Hamiltonian for a 1D chain.
H = J Σᵢ (XᵢXᵢ₊₁ + YᵢYᵢ₊₁ + ZᵢZᵢ₊₁)
Parameters:
Returns: Collection of Pauli terms
Create a Heisenberg model Hamiltonian for a 1D chain. H = J Σᵢ (XᵢXᵢ₊₁ + YᵢYᵢ₊₁ + ZᵢZᵢ₊₁) Parameters: - num-sites: Number of sites in the chain - coupling: Coupling strength J (default: 1.0) - periodic: Whether to use periodic boundary conditions (default: true) Returns: Collection of Pauli terms
(molecular-hydrogen-hamiltonian)(molecular-hydrogen-hamiltonian bond-distance)Create the molecular hydrogen (H₂) Hamiltonian in the STO-3G basis using Jordan-Wigner encoding.
This implementation provides the standard H₂ Hamiltonian used in quantum computing literature, mapped to a 4-qubit system via the Jordan-Wigner transformation. The qubit mapping follows the standard convention:
qubit 0: First spin orbital
qubit 1: Second spin orbital
qubit 2: Third spin orbital
qubit 3: Fourth spin orbital
The Hartree-Fock reference states |0011⟩ and |1100⟩ are degenerate in this representation, with the true ground state being a superposition that VQE should discover.
High-precision coefficients from Kandala et al. Nature (2017) ensure:
Parameters:
Returns: Collection of Pauli terms representing the H₂ molecular Hamiltonian with μHa precision
Create the molecular hydrogen (H₂) Hamiltonian in the STO-3G basis using Jordan-Wigner encoding. This implementation provides the standard H₂ Hamiltonian used in quantum computing literature, mapped to a 4-qubit system via the Jordan-Wigner transformation. The qubit mapping follows the standard convention: qubit 0: First spin orbital qubit 1: Second spin orbital qubit 2: Third spin orbital qubit 3: Fourth spin orbital The Hartree-Fock reference states |0011⟩ and |1100⟩ are degenerate in this representation, with the true ground state being a superposition that VQE should discover. High-precision coefficients from Kandala et al. Nature (2017) ensure: - Hartree-Fock energy: EXACTLY -1.117 Ha (μHa precision) - VQE ground state target: ~-1.137 Ha - Accuracy for quantum hardware implementations Parameters: - bond-distance: H-H bond distance in Angstroms (coefficient set is optimized for 0.735 Å) Returns: Collection of Pauli terms representing the H₂ molecular Hamiltonian with μHa precision
(post-optimization-analysis vqe-result analysis-options)Comprehensive post-optimization analysis using result framework.
This function performs detailed analysis of VQE results, including:
Parameters:
Returns: Comprehensive analysis report
Comprehensive post-optimization analysis using result framework. This function performs detailed analysis of VQE results, including: - Energy landscape analysis around optimal point - Quantum state characterization - Measurement statistics and confidence intervals - Hardware compatibility assessment Parameters: - vqe-result: Complete VQE result map - analysis-options: Options for analysis depth and methods Returns: Comprehensive analysis report
(variational-quantum-eigensolver backend options)Main VQE algorithm implementation.
This function orchestrates the VQE process, including ansatz creation, optimization, and execution on a quantum backend. It supports various ansatz types and optimization methods, allowing for flexible configuration based on the problem and available resources.
Supported ansatz types:
Supported optimization methods:
Parameters:
Returns: Map containing VQE results and analysis
Example: (variational-quantum-eigensolver backend {:hamiltonian [{:coefficient 1.0 :terms [[0 1]]} {:coefficient -0.5 :terms [[0 0] [1 1]]}] :ansatz-type :hardware-efficient :num-qubits 2 :num-layers 2 :optimization-method :adam :max-iterations 100 :tolerance 1e-5 :shots 2048})
Main VQE algorithm implementation.
This function orchestrates the VQE process, including ansatz creation,
optimization, and execution on a quantum backend.
It supports various ansatz types and optimization methods, allowing
for flexible configuration based on the problem and available resources.
Supported ansatz types:
- :hardware-efficient - Hardware-efficient ansatz with configurable layers and entangling gates
- :chemistry-inspired - Chemistry-inspired ansatz with excitation layers
- :uccsd - UCCSD ansatz for chemistry problems
- :symmetry-preserving - Symmetry-preserving ansatz for fermionic systems
- :custom - Custom ansatz function provided in options
Supported optimization methods:
- :gradient-descent - Basic gradient descent with parameter shift gradients
- :adam - Adam optimizer with parameter shift gradients
- :quantum-natural-gradient - Quantum Natural Gradient using Fisher Information Matrix
- :nelder-mead - Derivative-free Nelder-Mead simplex method
- :powell - Derivative-free Powell's method
- :cmaes - Covariance Matrix Adaptation Evolution Strategy (robust)
- :bobyqa - Bound Optimization BY Quadratic Approximation (handles bounds well)
- :gradient - Fastmath gradient-based optimizers (not available in this version)
Parameters:
- backend: Quantum backend implementing QuantumBackend protocol
- options: Additional options map for execution
- :optimization-method - Optimization method to use (default: :adam)
- :max-iterations - Maximum iterations for optimization (default: 500)
- :tolerance - Convergence tolerance (default: 1e-6)
- :ansatz-type - Ansatz type to use (default: :hardware-efficient)
- :num-qubits - Number of qubits in the circuit (default: 2)
- :num-layers - Number of layers for hardware-efficient ansatz (default: 1)
- :num-excitation-layers - Number of excitation layers for chemistry-inspired ansatz (default: 1)
- :num-excitations - Number of excitations for UCCSD ansatz (default: 2)
- :num-particles - Number of particles for symmetry-preserving ansatz (default: 2)
- :shots - Number of shots for circuit execution (default: 1024)
Returns:
Map containing VQE results and analysis
Example:
(variational-quantum-eigensolver backend
{:hamiltonian [{:coefficient 1.0 :terms [[0 1]]}
{:coefficient -0.5 :terms [[0 0] [1 1]]}]
:ansatz-type :hardware-efficient
:num-qubits 2
:num-layers 2
:optimization-method :adam
:max-iterations 100
:tolerance 1e-5
:shots 2048})cljdoc builds & hosts documentation for Clojure/Script libraries
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