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QuantumCollocation.jl

QuantumCollocation.jl is a Julia package for solving quantum optimal control problems using direct collocation methods. It transforms continuous-time quantum control into finite-dimensional nonlinear programs (NLPs) solved efficiently with Ipopt.

Quick Start

Installation

using Pkg
Pkg.add("QuantumCollocation")

Or from the Julia REPL, press ] to enter package mode:

pkg> add QuantumCollocation

30-Second Example

Here's a complete example optimizing a Hadamard gate on a qubit:

using QuantumCollocation
using PiccoloQuantumObjects

# Define system: drift + 2 control Hamiltonians
H_drift = 0.1 * PAULIS.Z
H_drives = [PAULIS.X, PAULIS.Y]
drive_bounds = [1.0, 1.0]  # symmetric bounds
sys = QuantumSystem(H_drift, H_drives, drive_bounds)

# 2. Create quantum trajectory. defines problem: system, target gate, timesteps
U_goal = GATES[:H]
T = 10.0
qtraj = UnitaryTrajectory(sys, U_goal, T) # creates zero pulse internally

# 3. Build optimization problem
N = 51  # number of timesteps
qcp = SmoothPulseProblem(qtraj, N; Q=100.0, R=1e-2)

# Solve!
solve!(qcp; options=IpoptOptions(max_iter=100))

# Check result
traj = get_trajectory(qcp)
println("Fidelity: ", fidelity(qcp))

That's it! You've optimized control pulses for a quantum gate.

What Can QuantumCollocation Do?

  • Unitary gate optimization - Find pulses to implement quantum gates
  • Open quantum systems - Find pulses for Lindbladian dynamics
  • State transfer - Drive quantum states to target states
  • Minimum time control - Optimize gate duration
  • Robust control - Account for system uncertainties
  • Multilevel systems - Handle transmons, bosonic codes, etc.
  • Leakage suppression - Constrain populations in unwanted levels
  • Custom constraints - Add your own physics constraints

Overview

QuantumCollocation.jl sets up and solves quantum control problems as nonlinear programs (NLPs). A generic quantum control problem looks like:

\[\begin{aligned} \arg \min_{\mathbf{Z}}\quad & J(\mathbf{Z}) \\ \text{s.t.}\qquad & \mathbf{f}(\mathbf{Z}) = 0 \\ & \mathbf{g}(\mathbf{Z}) \le 0 \end{aligned}\]

where $\mathbf{Z}$ is a trajectory containing states and controls from NamedTrajectories.jl.

We provide problem templates for common quantum control tasks. These templates construct a DirectTrajOptProblem from DirectTrajOpt.jl with appropriate objectives, constraints, and dynamics.

Problem Templates

Problem templates are organized by the type of quantum system being controlled:

General Problem Templates

See the Problem Templates Overview for a detailed comparison and selection guide.

How It Works

Direct Collocation

QuantumCollocation uses direct collocation - discretizing continuous-time dynamics into constraints at discrete time points (knot points). For example, a smooth pulse problem for a unitary gate:

\[\begin{aligned} \arg \min_{\mathbf{Z}}\quad & |1 - \mathcal{F}(U_N, U_\text{goal})| \\ \text{s.t.}\qquad & U_{k+1} = \exp\{- i H(u_k) \Delta t_k \} U_k, \quad \forall\, k \\ & u_{k+1} = u_k + \dot{u}_k \Delta t_k \\ & \dot{u}_{k+1} = \dot{u}_k + \ddot{u}_k \Delta t_k \\ & |u_k| \le u_\text{max}, \quad |\ddot{u}_k| \le \ddot{u}_\text{max} \end{aligned}\]

The dynamics between knot points $(U_k, u_k)$ and $(U_{k+1}, u_{k+1})$ become nonlinear equality constraints. States and controls are free variables optimized by the NLP solver.

Key Features

  • Efficient gradients - Sparse Jacobians and Hessians via automatic differentiation
  • Flexible constraints - Add custom physics, leakage suppression, robustness
  • Multiple integrators - Exponential, Pade, time-dependent dynamics
  • Extensible - Easy to add new objectives, constraints, and problem templates

Next Steps

QuantumCollocation.jl is part of the Piccolo ecosystem:

Problem templates give the user the ability to add other constraints and objective functions to this problem and solve it efficiently using Ipopt.jl and MathOptInterface.jl under the hood (support for additional backends coming soon!).