converts a binary state vector into a bra-ket notation string note: reverses qubit order for presentation

converts a binary state vector into an integer id following the package conventions valid ints are from 0-to-2^n-1

converts a binary state vector (0/1) into an spin state vector (-1/1)

ground state of sumi A(0) Xi where A(0) > 0 and B(0) = 0

converts a integer id into a binary state vector following the package conventions valid ints are from 0-to-2^n-1 pad should be the total number qubits in the system

converts a integer id into a spin state vector following the package conventions valid ints are from 0-to-2^n-1 pad should be the total number qubits in the system

given a 2^n vector of probably values, prints each value and its associated state vector. limit is used to limit the total number of states that are printed. sort is used to re-order the states by most likely instead of the default which is numerical order from 0-to-(2^n-1)

converts a spin state vector (-1/1) into an binary state vector (0/1)

converts a spin state vector (-1/1) into bra-ket notation (↓/↑) note: reverses qubit order for presentation

converts a spin state vector into an integer id following the package conventions valid ints are from 0-to-2^n-1

given a 2^n-by-2^n density matrix returns the probably of seeing each of the 2^n states on z-basis.

Function to build the transverse field Ising model hamiltonian at a given unitless timestep s.

Arguments: isingmodel - ising model represented as a dictionary. The qubits and couplings are represented as tuples, and the weights are numbers. For Example: im = Dict((1,) => 1, (2,) => 0.5, (1,2) => 2) annealingschedule - The annealing schedule, of the form given by the struct s - the imaginary timestep. This should usually be in the range from 0.0-to-1.0

Main function for performing quantum annealing simulation via a Magnus Expansion (second order). Noise can be simulated by running multiple times with randomized constant fields.

Arguments: isingmodel - ising model represented as a dictionary. The qubits and couplings are represented as tuples, and the weights are numbers. For Example: im = Dict((1,) => 1, (2,) => 0.5, (1,2) => 2) annealingschedule - The annealing schedule, of the form given by the struct

Parameters: initialstate - Initial state vector. Defaults to uniform superposition state on n qubits constantfieldx - vector of constant biases in the X basis on each qubit. Default is zeros(n) constantfieldz - vector of constant biases in the Z basis on each qubit. Default is zeros(n) The parameters `meantolandmax_tolspecify the desired simulation accuracy. Thesilence` parameter can be used to suppress the progress log.

a generic Magnus expansion solver with a fixed number of time steps

a Magnus expansion implementation simulate specialized to two quadratic functions of orders 1 to 4

simulator that uses the DifferentialEquations.jl differential equation solver to solve the Schrodinger Equation, rather than the Magnus Expansion. This simulator can run into issues at higher anneal times. The API is the same as for the simulate function.

Arguments: isingmodel - ising model represented as a dictionary. The qubits and couplings are represented as tuples, and the weights are numbers. For Example: im = Dict((1,) => 1, (2,) => 0.5, (1,2) => 2) annealingschedule - The annealing schedule, of the form given by the struct reltol - the relative tolerance that will be used in the ODE simulation

Parameters: initialstate - Initial state vector. Defaults to uniform superposition state on n qubits constantfieldx - vector of constant biases in the X basis on each qubit. Default is zeros(n) constantfield_z - vector of constant biases in the Z basis on each qubit. Default is zeros(n)

A simplified interface to the simulate_de routine that determines suitable tolerance values to ensure a high accuracy simulation. The parameters mean_tol and max_tol specify the desired simulation accuracy. The silence parameter can be used to suppress the progress log.

A data structure containing two uni-variate functions defined in the domain of 0.0-to-1.0. The A function drives the evolution of the X basis and the B function drives the evolution of the Z basis. init_default is a uni-variate function that given an integer n builds a initial state vector for an n qubit system.

An AnnealingSchedule implementing a simple linear form

An AnnealingSchedule implementing a simple quadratic form

An AnnealingSchedule implementing uniform circular motion with an analytical solution on a single qubit

An AnnealingSchedule approximating those used in hardware by D-Wave Systems

NOTE: users are strongly encouraged to download annealing schedules for specific D-Wave Systems devices and load them using parse_dwave_annealing_schedule.

given an Ising model computes a mapping from energy values to collections of state integers

given an Ising model computes a mapping from state integers to energy values

given a state vector of spin values and an Ising model computes the energy of that spin configuration

given an Ising model prints state strings by ascending energy levels. limit is used the stop the printing after a number of energy levels have been presented (limit <= 0 will print all states).

Function to modify an existing annealing schedule to use a customized annealing schedule (asch). These parameters are the same as those used in a dwisc call or a dwave schedule. Inputs: annealingschedule - annealingschedule

Parameters: asch - This is the annealing-schedule parameter. This is a list of tuples of the form [(s₀,seffective₀), (s₀,seffective₁), ..., (sₙ,s_effectiveₙ)].

ground state of sumi A(0)Xi where A(0) < 0 and B(0) = 0

This function reads in a bqpjson file and generates the ising model dictionary inputs: bqpjson::String - a bqpjson file (v1.0.0) that can be run on D-Wave hardware outputs: n - number of qubits ising_model::Dict{Tuple => Float64} - Dictionary of qubits and couplings to weights mapping:Dict{Int => Int} - mapping of the qubits in the bqpjson file to simulation qubits

function to take a CSV of DWave annealing schedule values and convert it into an annealing schedule usable by the simulator. valid values for interpolation are :none, :linear, :quadratic

function that allows for simulation from a bqpjson data file

function that allows for simulation with x and z noise from a bqpjson data file. The x_bias and z_bias parameters provide vectors of noise realizations.