QuantumClifford.jl

QuantumClifford.jl is a Julia library for simulation of Clifford circuits, which are a subclass of quantum circuits that can be efficiently simulated on a classical computer.

This library uses the tableaux formalism^[1] with the destabilizer improvements^[2]. Pauli frames are supported for faster repeated simulation of noisy circuits. Various symbolic and algebraic tools for manipulating, converting, and visualizing states and circuits are also implemented.

The library consists of two main parts: Tools for working with the algebra of Stabilizer Tableaux and tools specifically for efficient Circuit Simulation.

Stabilizer Tableau Algebra

The Stabilizer Tableau Algebra component of QuantumClifford.jl efficiently handles pure and mixed stabilizer states of thousands of qubits, along with support for sparse or dense Clifford operations acting upon them. It provides operations such as canonicalization, projection, generation , and partial traces. The code is vectorized and multithreaded, offering fast, in-place, and allocation-free implementations. Tools for conversion to graph states and for visualization of tableaux are available.

See the Stabilizer Tableau Algebra manual or the curated list of useful functions.

Example Usage

julia> using QuantumClifford

julia> P"X" * P"Z"
-iY

julia> P"X" ⊗ P"Z"
+ XZ

julia> S"-XX
         +ZZ"
- XX
+ ZZ

julia> tCNOT * S"-XX
                 +ZZ"
- X_
+ _Z

Circuit Simulation

The circuit simulation component of QuantumClifford.jl enables Monte Carlo (or symbolic) simulations of noisy Clifford circuits. It provides three main simulation methods: mctrajectories, pftrajectories, and petrajectories. These methods offer varying levels of efficiency, accuracy, and insight.

Monte Carlo Simulations with Stabilizer Tableaux (`mctrajectories`)

The mctrajectories method runs Monte Carlo simulations using a Stabilizer tableau representation for the quantum states.

Monte Carlo Simulations with Pauli Frames (`pftrajectories`)

The pftrajectories method runs Monte Carlo simulations of Pauli frames over a single reference Stabilizer tableau simulation. This approach is much more efficient but supports a smaller class of circuits.

Symbolic Depth-First Traversal of Quantum Trajectories (`petrajectories`)

The petrajectories method performs a depth-first traversal of the most probable quantum trajectories, providing a fixed-order approximation of the circuit's behavior. This approach gives symbolic expressions for various figures of merit instead of just a numeric value.