Algorithms Library Overview

quantum_debugger.algorithms is a library of genuine, gate-based quantum algorithms on the state-vector simulator. Every routine is verified against its known outcome (exact amplitudes, exact factoring, exact eigenvalues, or a matching analytic curve). This page indexes the whole library; each entry links to a worked example in the Algorithms guide.

from quantum_debugger.algorithms import grover_search, shor_factor, trotter_evolve

Search & oracle algorithms

Function	What it does
`grover`, `grover_search`, `optimal_iterations`	Grover unstructured search
`grover_solve`	Find an input satisfying an arbitrary boolean predicate (SAT)
`grover_minimize`	Durr-Hoyer adaptive minimization of a cost function
`amplitude_amplification`, `optimal_amplification_iterations`	Grover for any state prep
`bernstein_vazirani`	Recover a hidden bit-string in one query
`deutsch`	Deutsch’s algorithm: constant vs balanced 1-bit function (1 query)
`deutsch_jozsa`, `constant_oracle`, `balanced_oracle`	Constant vs balanced (n-bit)
`simon`, `simon_oracle`	Hidden XOR-mask (period) finding

Fourier, phase estimation & factoring

Function	What it does
`qft`, `apply_qft`, `apply_inverse_qft`, `qft_matrix`	Quantum Fourier transform
`estimate_phase`, `phase_estimation_circuit`	QPE on the phase gate
`iterative_phase_estimation`	Single-ancilla (Kitaev) QPE
`unitary_eigenphase`, `hermitian_eigenvalue`	QPE for arbitrary operators (spectroscopy)
`period_finding`, `shor_factor`	Shor’s algorithm (period finding + factoring)
`quantum_counting`, `amplitude_estimation`	Count marked states / estimate amplitude

Simulation & chemistry

Function	What it does
`trotter_evolve`, `trotter_circuit`	Trotter-Suzuki Hamiltonian simulation
`hamiltonian_matrix`, `pauli_term_matrix`	Build a Hamiltonian from Pauli strings
`variational_ground_state`	Hardware-efficient VQE ground-state solver
`tfim_hamiltonian`, `heisenberg_hamiltonian`	Ready-made spin Hamiltonians
`hhl`	Quantum linear-systems solver
`quantum_walk`	Discrete-time coined quantum walk

Optimization

Function	What it does
`solve_maxcut`, `brute_force_maxcut`	QAOA MaxCut solver + exact reference
`grover_minimize`	Grover adaptive minimization

Error correction & benchmarking

Function	What it does
`bit_flip_code`, `phase_flip_code`, `shor_code`	Stabilizer QEC codes
`repetition_code_error_rate`	Logical error rate vs the QEC threshold
`randomized_benchmarking`, `single_qubit_clifford_group`	Average gate fidelity

Circuit synthesis & arithmetic

Function	What it does
`zyz_decompose`, `abc_decomposition`	Single-qubit / controlled-U decomposition
`kak_decompose`, `canonical_coordinates`	Two-qubit Cartan (KAK) decomposition
`toffoli_gates`, `fredkin_gates`, `mcx_gates`	Multi-controlled gate synthesis
`qft_add`, `quantum_adder`	Draper QFT adder (constant / two-register)
`qft_subtract`, `quantum_compare`	QFT subtractor and comparator

Entanglement, protocols & foundations

Function	What it does
`ghz_state`, `w_state`, `graph_state`	Canonical entangled-state preparation
`teleport`, `superdense_coding`, `entanglement_swap`	Communication protocols
`swap_test`	Estimate the overlap of two states
`chsh_value`, `chsh_game`, `correlator`, `bell_state`	Bell inequality + nonlocal game
`phase_sensitivity`, `parity_signal`, `quantum_fisher_information`	GHZ metrology
`bb84`	BB84 quantum key distribution

Quantum Singular Value Transformation (QSVT) & Modern Primitives

Function	What it does
`qsp_unitary`, `qsp_response`, `chebyshev_via_qsp`, `signal_operator`	Quantum Signal Processing (1-qubit designable polynomials)
`block_encode`, `top_left_block`, `is_block_encoding`	Unitary block encoding of arbitrary matrices
`qubitization_walk`, `chebyshev_of_matrix`	Qubitization walk realizing matrix Chebyshev polynomials
`lcu_block_encoding`, `lcu_matrix`	Linear Combination of Unitaries (PREPARE / SELECT)
`qsvt_transform`, `qsvt_scalar_response`	Quantum Singular Value Transformation (eigenvalue-wise polynomial)
`hamiltonian_simulation_qsvt`, `matrix_function_chebyshev`	Real-time unitary simulation and smooth Chebyshev matrix functions
`solve_linear_system_qsvt`, `matrix_inverse_qsvt`	Quantum linear systems solver ($A x = b$) via polynomial inversion
`matrix_sign_qsvt`, `spectral_projector_qsvt`	Matrix sign function and spectral cut projections
`matrix_sqrt_qsvt`, `matrix_power_qsvt`, `matrix_exp_qsvt`	Fractional/negative matrix powers and matrix exponentials
`ground_state_projector_qsvt`, `gibbs_state_qsvt`	Low-energy ground state filtering and thermal states
`spectral_moments`, `density_of_states_kpm`	Kernel Polynomial Method (KPM) moment estimation and DOS
`eigenvalue_count_in_interval`, `trace_of_function`	Interval eigenvalue counting and trace estimation
`amplitude_amplification_qsvt`	Grover amplitude amplification as scalar QSVT

See the QSVT Guide for detailed theory and examples.