Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2610.24160

Trajectree - A quantum trajectory-based quantum circuit simulator

Ansh Singal, Allen Zang, Jordan Thomas, Alexander Kolar, Anirudh Ramesh, Joaquin Chung, Rajkumar Kettimuthu, Prem Kumar

quant-phSubmitted Oct 16, 2026• Announced Oct 20, 2026• 0 citations
arXivHTMLPDF

Abstract

We introduce Trajectree, a quantum trajectory-based quantum circuit simulator that uses a novel, state-saving partial execution of the quantum circuits to simulate broad and deep noisy quantum circuits efficiently. Trajectree can efficiently generate a large number of Monte Carlo samples by saving partially executed trajectories. We conduct extensive performance analysis of the Trajectree approach, proving the utility of the trajectory saving scheme for simulations of open quantum systems. Using this architecture, we show that Trajectree can simulate standard benchmark noisy circuits over five times faster than Google's QSim, a part of the Cirq package. We also analyze Trajectree's performance for simulating quantum optical systems relevant to communication and computing applications. We demonstrate applications of the optical backend to simulate three optical experiments: CHSH Bell test, entanglement swapping, and optical CNOT gate. This shows Trajectree's potential for simulating noisy qudit and optical systems efficiently.

Comments
15 pages, 22 figures

Related papers

Simulations of Quantum Circuits with Approximate Noise using qsim and Cirq

Sergei V. Isakov, Dvir Kafri, Orion Martin +15 more

We introduce multinode quantum trajectory simulations with qsim, an open source high performance simulator of quantum circuits. qsim can be used as a backend of Cirq, a Python software library for writing quantum circuits. We present a novel delayed inner product algorithm for quantum trajectories which can result in an order of magnitude speedup for low noise simulation. We also provide tools to use this framework in Google Cloud Platform, with high performance virtual machines in a single mode or multinode setting. Multinode configurations are well suited to simulate noisy quantum circuits with quantum trajectories. Finally, we introduce an approximate noise model for Google's experimental quantum computing platform and compare the results of noisy simulations with experiments for several quantum algorithms on Google's Quantum Computing Service.

arXiv:2111.02396•Nov 3, 2021•17 citations

Approximation Algorithm for Noisy Quantum Circuit Simulation

Mingyu Huang, Ji Guan, Wang Sheng Fang +1 more

Simulating noisy quantum circuits is vital in de-signing and verifying quantum algorithms in the current NISQ (Noisy Intermediate-Scale Quantum) era, where quantum noise is unavoidable. However, it is much more inefficient than the classical counterpart because of the quantum state explosion problem (the dimension of state space is exponential in the number of qubits) and the complex (non-unitary) representation of noises. Consequently, only noisy circuits with up to about 50 qubits can be simulated approximately well. To improve the scalability of the circuits that can be simulated, this paper introduces a novel approximation algorithm for simulating noisy quantum circuits when the noisy effectiveness is insignificant. The algorithm is based on a new tensor network diagram for the noisy simulation and uses the singular value decomposition to approximate the tensors of quantum noises in the diagram. The contraction of the tensor network diagram is implemented on Google's TensorNetwork. The effectiveness and utility of the algorithm are demonstrated by experimenting on a series of practical quantum circuits with realistic superconducting noise models. As a result, our algorithm can approximately simulate quantum circuits with up to 225 qubits and 20 noises (within about 1.8 hours). In particular, our method offers a speedup over the commonly-used approximation (sampling) algorithm - quantum trajectories method [1]. Furthermore, our approach can significantly reduce the number of samples in the quantum trajectories method when the noise rate is small enough,

arXiv:2211.17028•Design, Automation, and Test in Europe•Mar 25, 2024•1 citation

Real-Time Sign-Problem-Suppressed Quantum Monte Carlo Algorithm for Noisy Quantum Circuit Simulations

Tong Shen, Daniel A. Lidar

We present a real-time quantum Monte Carlo algorithm that simulates the dynamics of open quantum systems by stochastically compressing and evolving the density matrix under both Markovian and non-Markovian master equations. Our algorithm uses population dynamics to continuously suppress the sign problem, preventing its accumulation throughout the evolution for a broad class of noisy-circuit Liouvillians of practical and experimental interest. We apply it to a variety of quantum circuits and demonstrate significant speedups and scaling improvements over state-of-the-art quantum trajectory methods and convergence to exact solutions even in non-Markovian regimes where trajectory methods fail. Our approach improves the efficiency of classical simulation of gate-based quantum computing, quantum annealing, and general open system dynamics.

arXiv:2502.18929•Physical Review Letters•Apr 30, 2026•3 citations

Speed-oriented quantum circuit backend

Sören Wilkening

We present a new software package for efficient quantum circuit generation, designed to achieve optimal runtime performance. Despite being in an early stage of development, our implementation demonstrates significant advantages over existing tools. Using the quantum Fourier transform (QFT) as a benchmark, we show that our backend can generate circuits for systems with up to 2000 qubits faster than widely used frameworks such as Qiskit and Q#. This improvement is particularly relevant for applications where classical preprocessing time, including circuit generation, must be minimized to not diminish any potential quantum advantage - for example, in combinatorial optimization tasks. Additionally, our software provides high-level primitives for bit- and integer-level manipulations, offering a simplified interface for integration with high-level quantum programming languages.

quant-pharXiv:2604.21656•Apr 24, 2026•0 citations

QiliSim: A C++ Quantum Simulator for Digital/Analog Workflows

Luke Mortimer, D. Babal, Vyron Vasileiadis +1 more

This work presents QiliSim, the native C++ simulation backend of QiliSDK, an open-source Python framework for digital and analog quantum computing. QiliSim supports quantum circuits, Hamiltonian time evolution, and analog-digital quantum reservoirs through a common interface, allowing users to test quantum algorithms before executing them on quantum hardware. The simulator provides statevector and density-matrix methods for digital workloads, alongside fixed-step and adaptive Runge–Kutta integrators, Krylov-subspace methods, and direct matrix exponentiation for analog evolution. Monte Carlo trajectories, mid-circuit measurements, and Kraus and Lindbladian noise models support the simulation of noisy quantum systems. Numerical methods and execution settings are selected through structured configuration objects, allowing the same quantum program to run with different simulation strategies without modifying its definition. The poster includes a circuit simulation example and performance comparisons for digital circuit sampling and quantum annealing. The reported benchmarks show competitive CPU performance against Qiskit Aer and Cirq for small to medium circuits, and faster execution than QuTiP and CUDA-Q dynamics for the tested annealing task at a target fidelity of 99%.

•Sep 14, 2026•0 citations

Establishing Convergence Thresholds for Pre-Trajectory Sampling with Batched Execution Across Random Quantum Circuits

Eskew, Taylor L., Gonthier, Jerome F., Patti, Taylor L. +1 more

A crucial aspect of validating quantum protocols is understanding the noise produced by quantum computing devices. Using simulations that can replicate this noise allows for a lower-cost alternative to hardware experiments. Stochastic, so-called "trajectory" methods are often used as a quadratically reduced approximation to density matrix simulations, but traditional implementations have limited sampling capacity and provide no error-based metadata. The Pre-Trajectory Sampling with Batched Execution (PTSBE) [Patti et al., 2025] algorithm provides a solution by combining fine-tuned, well-documented noise sampling with computational intermediate caching. While the original work is effective on quantum error correction circuits, its performance on general circuits has yet to be explored. This project gauges PTSBE on random quantum circuits to understand convergence behavior and accuracy compared to traditional methods. To accomplish this, an automated simulation pipeline was developed by using Apache Airflow and CUDA-Q to generate a collection of noisy circuits, run both exact and approximate simulations, and analyze error criteria across various qubit counts and circuit depths. Early tests have confirmed the system's ability to scale to 20-qubit circuits and produce accurate comparison data. Our work aims to provide guidance for researchers using PTSBE in noisy simulation environments, expanding its use beyond specific cases.

•Dec 4, 2025•0 citations
We introduce Trajectree, a quantum trajectory-based quantum circuit simulator that uses a novel, state-saving partial execution of the quantum circuits to simulate broad and deep noisy quantum circuits efficiently. Trajectree can efficiently generate a large number of Monte Carlo samples by saving partially executed trajectories. We conduct extensive performance analysis of the Trajectree approach, proving the utility of the trajectory saving scheme for simulations of open quantum systems. Using this architecture, we show that Trajectree can simulate standard benchmark noisy circuits over five times faster than Google's QSim, a part of the Cirq package. We also analyze Trajectree's performance for simulating quantum optical systems relevant to communication and computing applications. We demonstrate applications of the optical backend to simulate three optical experiments: CHSH Bell test, entanglement swapping, and optical CNOT gate. This shows Trajectree's potential for simulating noisy qudit and optical systems efficiently.
We introduce multinode quantum trajectory simulations with qsim, an open source high performance simulator of quantum circuits. qsim can be used as a backend of Cirq, a Python software library for writing quantum circuits. We present a novel delayed inner product algorithm for quantum trajectories which can result in an order of magnitude speedup for low noise simulation. We also provide tools to use this framework in Google Cloud Platform, with high performance virtual machines in a single mode or multinode setting. Multinode configurations are well suited to simulate noisy quantum circuits with quantum trajectories. Finally, we introduce an approximate noise model for Google's experimental quantum computing platform and compare the results of noisy simulations with experiments for several quantum algorithms on Google's Quantum Computing Service.
Simulating noisy quantum circuits is vital in de-signing and verifying quantum algorithms in the current NISQ (Noisy Intermediate-Scale Quantum) era, where quantum noise is unavoidable. However, it is much more inefficient than the classical counterpart because of the quantum state explosion problem (the dimension of state space is exponential in the number of qubits) and the complex (non-unitary) representation of noises. Consequently, only noisy circuits with up to about 50 qubits can be simulated approximately well. To improve the scalability of the circuits that can be simulated, this paper introduces a novel approximation algorithm for simulating noisy quantum circuits when the noisy effectiveness is insignificant. The algorithm is based on a new tensor network diagram for the noisy simulation and uses the singular value decomposition to approximate the tensors of quantum noises in the diagram. The contraction of the tensor network diagram is implemented on Google's TensorNetwork. The effectiveness and utility of the algorithm are demonstrated by experimenting on a series of practical quantum circuits with realistic superconducting noise models. As a result, our algorithm can approximately simulate quantum circuits with up to 225 qubits and 20 noises (within about 1.8 hours). In particular, our method offers a speedup over the commonly-used approximation (sampling) algorithm - quantum trajectories method [1]. Furthermore, our approach can significantly reduce the number of samples in the quantum trajectories method when the noise rate is small enough,
We present a real-time quantum Monte Carlo algorithm that simulates the dynamics of open quantum systems by stochastically compressing and evolving the density matrix under both Markovian and non-Markovian master equations. Our algorithm uses population dynamics to continuously suppress the sign problem, preventing its accumulation throughout the evolution for a broad class of noisy-circuit Liouvillians of practical and experimental interest. We apply it to a variety of quantum circuits and demonstrate significant speedups and scaling improvements over state-of-the-art quantum trajectory methods and convergence to exact solutions even in non-Markovian regimes where trajectory methods fail. Our approach improves the efficiency of classical simulation of gate-based quantum computing, quantum annealing, and general open system dynamics.
We present a new software package for efficient quantum circuit generation, designed to achieve optimal runtime performance. Despite being in an early stage of development, our implementation demonstrates significant advantages over existing tools. Using the quantum Fourier transform (QFT) as a benchmark, we show that our backend can generate circuits for systems with up to 2000 qubits faster than widely used frameworks such as Qiskit and Q#. This improvement is particularly relevant for applications where classical preprocessing time, including circuit generation, must be minimized to not diminish any potential quantum advantage - for example, in combinatorial optimization tasks. Additionally, our software provides high-level primitives for bit- and integer-level manipulations, offering a simplified interface for integration with high-level quantum programming languages.
This work presents QiliSim, the native C++ simulation backend of QiliSDK, an open-source Python framework for digital and analog quantum computing. QiliSim supports quantum circuits, Hamiltonian time evolution, and analog-digital quantum reservoirs through a common interface, allowing users to test quantum algorithms before executing them on quantum hardware. The simulator provides statevector and density-matrix methods for digital workloads, alongside fixed-step and adaptive Runge–Kutta integrators, Krylov-subspace methods, and direct matrix exponentiation for analog evolution. Monte Carlo trajectories, mid-circuit measurements, and Kraus and Lindbladian noise models support the simulation of noisy quantum systems. Numerical methods and execution settings are selected through structured configuration objects, allowing the same quantum program to run with different simulation strategies without modifying its definition. The poster includes a circuit simulation example and performance comparisons for digital circuit sampling and quantum annealing. The reported benchmarks show competitive CPU performance against Qiskit Aer and Cirq for small to medium circuits, and faster execution than QuTiP and CUDA-Q dynamics for the tested annealing task at a target fidelity of 99%.
A crucial aspect of validating quantum protocols is understanding the noise produced by quantum computing devices. Using simulations that can replicate this noise allows for a lower-cost alternative to hardware experiments. Stochastic, so-called "trajectory" methods are often used as a quadratically reduced approximation to density matrix simulations, but traditional implementations have limited sampling capacity and provide no error-based metadata. The Pre-Trajectory Sampling with Batched Execution (PTSBE) [Patti et al., 2025] algorithm provides a solution by combining fine-tuned, well-documented noise sampling with computational intermediate caching. While the original work is effective on quantum error correction circuits, its performance on general circuits has yet to be explored. This project gauges PTSBE on random quantum circuits to understand convergence behavior and accuracy compared to traditional methods. To accomplish this, an automated simulation pipeline was developed by using Apache Airflow and CUDA-Q to generate a collection of noisy circuits, run both exact and approximate simulations, and analyze error criteria across various qubit counts and circuit depths. Early tests have confirmed the system's ability to scale to 20-qubit circuits and produce accurate comparison data. Our work aims to provide guidance for researchers using PTSBE in noisy simulation environments, expanding its use beyond specific cases.