hhl

Documentation

Overview

Package hhl implements the Harrow-Hassidim-Lloyd algorithm for solving linear systems of equations Ax = b on a quantum computer.

Given a Hermitian matrix A (expressed as a PauliSum Hamiltonian) and a state preparation circuit for |b⟩, HHL estimates x = A⁻¹b encoded in the amplitudes of the output quantum state.

The algorithm uses three registers:

• 1 ancilla qubit for eigenvalue inversion flagging
• NumPhaseBits phase qubits for quantum phase estimation
• NumQubits system qubits representing the vector space

Index

• type Config
• type Result
  • func Run(ctx context.Context, cfg Config) (*Result, error)

Types

type Config

type Config struct {
	// Matrix is the Hermitian matrix A expressed as a Pauli Hamiltonian.
	Matrix pauli.PauliSum
	// RHS is the state preparation circuit for |b⟩.
	RHS *ir.Circuit
	// NumPhaseBits is the number of ancilla qubits for phase estimation precision.
	NumPhaseBits int
	// NumQubits is the number of system qubits (dimension of A is 2^NumQubits).
	NumQubits int
	// Shots is the number of measurement shots. Default: 1024.
	Shots int
}

Config specifies the HHL problem.

type Result

type Result struct {
	// Circuit is the full HHL circuit.
	Circuit *ir.Circuit
	// StateVector is the output state of the system register,
	// post-selected on ancilla = |1⟩ and phase register = |0⟩.
	StateVector []complex128
	// Success is the probability of the post-selection succeeding
	// (ancilla = |1⟩ and phase register = |0⟩).
	Success float64
}

Result holds HHL output.

func Run

func Run(ctx context.Context, cfg Config) (*Result, error)

Run executes the HHL algorithm.