pyrauli 0.9.0

A very fast and easy to use Quantum circuit simulator relying on Pauli propagation. Compatible with qiskit.

pyrauli: High-Performance Quantum Circuit Simulation

pyrauli is a high-performance Python package for quantum circuit simulation, powered by the C++ ProPauli library. It leverages the Heisenberg picture and a technique called Pauli back-propagation to efficiently calculate the expectation values of observables, making it particularly well-suited for certain classes of variational quantum algorithms and noise analysis.

Key Features

• High-Performance C++ Backend: Core simulation logic is implemented in C++ with OpenMP parallel execution support for maximum speed.
• Efficient Heisenberg Picture Simulation: Observables are evolved instead of the state vector, offering significant advantages for calculating expectation values on large systems.
• Direct Hamiltonian Evolution: Simulate time evolution exp(-iHt) for complex, multi-local Hamiltonians with a single optimized operation.
• Native Batch Processing: Simulate lists of observables in a single, parallelized call for massive throughput.
• Seamless Qiskit Integration: Use pyrauli as a drop-in backend or via the PyrauliEstimator primitive for modern, algorithm-focused development.
• Advanced Complexity Management: Fine-grained control over the simulation via customizable Truncator and SchedulingPolicy objects, with built-in truncation error tracking.
• Powerful Symbolic Toolkit: Simulate parameterized circuits with symbolic gate angles, noise strengths, and truncation thresholds.

Installation

pyrauli requires Python 3.9 or later. It can be installed from PyPI using pip.

Standard Installation

For core functionality:

pip install pyrauli

Installation with Qiskit Support

To enable the Qiskit integration features, install the [qiskit] extra:

pip install 'pyrauli[qiskit]'

Installation with Parallel Support

To enable high-performance parallel execution engine, install alongside an existing OpenMP compiler. Most user should not have to do anything to enable parallelism.

pip install pyrauli 

Note for macOS users: The parallel engine requires the OpenMP runtime. You may need to install it separately, e.g., via Homebrew: brew install libomp.

Quick Start

Simulate a simple 2-qubit Bell state circuit and calculate the expectation value of the $Z \otimes I$ observable.

import pyrauli

# 1. Initialize a 2-qubit circuit
circuit = pyrauli.Circuit(2)

# 2. Add quantum operations
circuit.add_operation("H", 0)      # Hadamard on qubit 0
circuit.add_operation("CX", 0, 1)  # CNOT with control 0, target 1

# 3. Define an observable
# Here, we measure the Pauli Z observable on qubit 0
observable = pyrauli.Observable("ZI")

# 4. Run the simulation
# This evolves the observable backward through the circuit
final_observable = circuit.run(observable)

# 5. Retrieve the final expectation value
# The expectation value is calculated with respect to the initial |00...0> state
expectation_value = final_observable.expectation_value()

print(f"Final observable: {final_observable}")
print(f"Expectation value: {expectation_value}")
print(f"Truncation error: {final_observable.truncate_error()}") # 0 here

# Expected output:
# Final observable: +1 XI
# Expectation value: 0.0
# Truncation error: 0.0

Qiskit Backend Usage

from qiskit.circuit import QuantumCircuit, Parameter
from qiskit.transpiler import generate_preset_pass_manager
from qiskit.quantum_info import SparsePauliOp
from pyrauli import PBackend

# Create a parameterized Qiskit circuit
theta = Parameter('theta')
qc = QuantumCircuit(2)
qc.h(0)
qc.rz(theta, 0)
qc.cx(0, 1)

# Define an observable and instantiate the backend
obs = SparsePauliOp("ZI")
backend = PBackend()

# transpilation is supported (but not needed here)
pm = generate_preset_pass_manager(backend)
isa_qc = pm.run(qc)

# Run using the PUB (Primitive Unified Bloc) format
job = backend.run([(qc, obs, [3.14])])
result = job.result()
ev = result[0].data.evs[0]

print(f"Expectation value: {ev}")

Advanced Usage: Direct Hamiltonian Evolution

pyrauli excels at simulating time evolution under complex, non-local Hamiltonians. The eiht method allows you to apply the operation exp(-iHt) in a single step, where H is a multi-qubit Pauli string. This is significantly more efficient and expressive than decomposing the operation into standard gates.

The following example simulates an 8-qubit system evolving under a 4-local Wen Plaquette operator, H = X_0 Z_1 X_4 Z_5.

import pyrauli
import math

# 1. Define simulation parameters
n_qubits = 8
time = 0.5

# 2. Define the Hamiltonian axis as a list of Pauli strings
# This corresponds to the operator H = X_0 Z_1 X_4 Z_5
hamiltonian_axis = ["X", "Z", "I", "I", "X", "Z", "I", "I"]

# 3. Build the circuit
circuit = pyrauli.Circuit(n_qubits)

# Apply the Hamiltonian evolution in a single, efficient operation
circuit.eiht(hamiltonian_axis, time)

# 4. Define an observable to measure
observable = pyrauli.Observable("ZIIIIIII") # Z on qubit 0

# 5. Run the simulation
ev, err = circuit.expectation_value(observable)

print(f"Expectation value of Z_0 after evolution: {ev:.4f}")

Documentation

For comprehensive information, including tutorials, how-to guides, and the full API reference, please visit the official documentation: https://zefresk.github.io/pyrauli/

benchmarks

pyrauli latest benchmarks results are available here: https://zefresk.github.io/pyrauli/dev/bench/

References

This work is based on and implements ideas from the following articles:

• Pauli Propagation: A Computational Framework for Simulating Quantum Systems, by Manuel S. Rudolph, Tyson Jones, Yanting Teng, Armando Angrisani, Zoë Holmes https://arxiv.org/abs/2505.21606

• Efficient simulation of parametrized quantum circuits under non-unital noise through Pauli backpropagation, by Victor Martinez, Armando Angrisani, Ekaterina Pankovets, Omar Fawzi, Daniel Stilck França https://arxiv.org/abs/2501.13050