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

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Modeling quantum information systems

Paul E. Black, Andrew W. Lane

Published Aug 24, 2004• 6 citations
Publisher

Abstract

A simulator for quantum information systems cannot be both general, that is, easily used for every possible system, and efficient. Therefore, some systems will have aspects which can only be simulated by cunning modeling. On the other hand, a simulation may conveniently do extra-systemic processing that would be impractical in a real system. We illustrate with examples from our quantum computing simulator, QCSim. We model the [3,1] Hamming code in the presence of random bit flip or generalized amplitude damping noise, and calculate the expected result in one simulation run, as opposed to, say, a Monte Carlo simulation, and keep the original state to compute the chance of successful transmission, too. We also model the BB84 protocol with eavesdropping and random choice of basis and compute the chance of information received faithfully. Finally, we present our simulation of teleportation as an example of the trade-off between complexity of the simulation model and complexity of simulation inputs and as an example of modeling measurements and classical bits.

DOI
10.1117/12.537667

Related papers

Efficient quantum circuit simulation.

John P. Hayes, Igor L. Markov, George F. Viamontes

Quantum-mechanical phenomena are playing an increasing role in information processing as transistor sizes approach the nanometer level, while the securest forms of communication rely on quantum data encoding. When they involve a finite number of basis states, these phenomena can be modeled as quantum circuits, the quantum analogue of conventional or classical logic circuits. Simulation of quantum circuits can therefore be used as a tool to evaluate issues in the design of quantum information processors. Unfortunately, simulating such phenomena efficiently is exceedingly difficult. The matrices representing quantum operators (gates) and vectors modeling quantum states grow exponentially with the number of quantum bits. The information represented by quantum states and operators often exhibits structure that can be exploited when simulating certain classes of quantum circuits. We study the development of simulation methods that run on classical computers and take advantage of such repetitions and redundancies. In particular, we define a new data structure for simulating quantum circuits called the quantum information decision diagram (QuIDD). A QuIDD is a compressed graph representation of a vector or matrix and permits computations to be performed directly on the compressed data. We develop a comprehensive set of algorithms for operating on QuIDDs in both the state-vector and density-matrix formats, and evaluate their complexity. These algorithms have been implemented in a general-purpose simulator program for quantum-mechanical applications called QuIDDPro. Through extensive experiments conducted on representative quantum simulation applications, including Grover's search algorithm, error characterization, and reversible circuits, we demonstrate that QuIDDPro is faster than other existing quantum-mechanical simulators such as the National Institute of Standards and Technology's QCSim program, and is far more memory-efficient. Using QuIDDPro, we explore the advantages of quantum computation over classical computation, simulate quantum errors and error correction, and study the impact of numerical precision on the fidelity of simulations. We also develop several novel algorithms for testing quantum circuit equivalence and compare them empirically. The QuIDDPro software is equipped with a user-friendly interface and is distributed with numerous example scripts. It has been used as a laboratory supplement for quantum computing courses at several universities.

•Jan 1, 2007•15 citations

Quantum information processing

Pieter Kok, Brendon W. Lovett

In general, all forms of information processing can be considered in a quantum mechanical context, including for example communication, channel capacities, and the quantum limits to information extraction. In this chapter we introduce the basic features of quantum information processing. We first present qubits as abstractions of two-level addressable quantum systems, before generalizing this concept to higher-dimensional qudit systems, and continuous variables. We introduce the stabilizer formalism towards the beginning of our discussion as a convenient way to track quantum information. In Section 2.2 we derive the no-cloning theorem, which leads us to cryptography, teleportation, and quantum repeaters. Section 2.3 describes quantum computing with qubits. We start with a brief description of the circuit model, and use it to define cluster states and the one-way model. We study the properties of cluster states and discuss error correction. In the last section we introduce quantum computing over continuous variables. Quantum information Classically, information is carried by ‘bits’, which are physical systems that have two (macroscopic) states denoted by 0 and 1. These bits are described classically, which immediately raises the question of how we should extend this information-theoretic description to the quantum mechanical case. This will lead to the quantum unit of information, the quantum bit or ‘qubit’. 2.1.1 Classical and quantum bits We can define the qubit as a two-dimensional quantum system, which means that the state space of the system is a two-dimensional complex Hilbert space ℋ.

Cambridge University Press eBooks•Apr 22, 2010•0 citations

Models to Reduce the Complexity of Simulating a Quantum Computer

Kevin Obenland, Alvin M. Despain

Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation is a useful tool for determining the feasibility of quantum computers in the presence of errors. The size of a quantum computer that can be simulat ed is small because faithfully modeling a quantum computer requires an exponential amount of storage and number of operations. In this paper we define simulation models to study the feasibility of quantum computers. The most detailed of these models is based directly on a proposed imple mentation. We also define less detailed models which are exponentially less complex but still pro duce accurate results. Finally we show that the two different types of errors, decoherence and inaccuracies, are uncorrelated. This decreases the number of simulations which must be per formed.

arXiv:quant-ph/9712004•Dec 2, 1997•3 citations

Simulating noisy quantum protocols with quantum trajectories

Gabriel G. Carlo, Giuliano Benenti, Giulio Casati +1 more

The theory of quantum trajectories is applied to simulate the effects of quantum noise sources induced by the environment on quantum information protocols. We study two models that generalize single qubit noise channels like amplitude damping and phase flip to the many-qubit situation. We calculate the fidelity of quantum information transmission through a chaotic channel using the teleportation scheme with different environments. In this example, we analyze the role played by the kind of collective noise suffered by the quantum processor during its operation. We also investigate the stability of a quantum algorithm simulating the quantum dynamics of a paradigmatic model of chaos, the baker's map. Our results demonstrate that, using the quantum trajectories approach, we are able to simulate quantum protocols in the presence of noise and with large system sizes of more than 20 qubits.

arXiv:quant-ph/0402102•Physical Review A•Jun 18, 2004•28 citations

Asymmetric quantum error correction efficiently tackles application-specific noise effects

Abhishek Yadav, Peter K. Schuhmacher, Michael Epping

Noise is a major challenge for current quantum computers. It can be broadly categorized into bit-flip and phase-flip errors. These two types do not necessarily affect the executed algorithm, thus also the application, in the same way. We illustrate this general effect for the example of the quantum approximate optimization algorithm (QAOA) applied to a small instance of the flight-gate assignment (FGA) problem. We compare bit-flip and phase-flip Pauli noise under both layer-level and gate-level noise models, using two circuit decompositions of the same ideal QAOA unitary: a CNOT-based decomposition and a native-$R_{ZZ}$ decomposition. In the simulations, bit-flip noise produces the larger degradation in the performance of the quantum optimization. The asymmetry is most visible in the layer-level and native-$R_{ZZ}$ simulations. We explain this by how the errors affect mixing, final measurements, and how they propagate inside the circuit. We then exploit these insights to tackle noise particularly efficiently using asymmetric error-correcting codes. As an illustration, we use the quantum parity code (QPC), a generalization of the 9-qubit Shor code, and show that a smaller asymmetric code can achieve nearly the same improvement as a larger symmetric choice. This demonstrates that error-correction resources should be assigned not only according to physical error rates, but also according to how strongly each error channel affects the application. As a result, asymmetric quantum error correction proves useful even in cases where the noise model is symmetric. Finally, we discuss how information about the noise obtained through calibration can be exploited in our approach.

quant-pharXiv:2609.07235•Sep 8, 2026•0 citations

Quantum Computers and Their Simulation.

Thomas Lippert

Quantum computing is based on the exploitation of quantum effects to perform some important computations more efficiently than ever possible on classical computers. Well known quantum algorithms are Shors polynomial time factoring algorithm and Grovers data base search scheme. Their potential is due to the parallelism of a quantum computation increasing exponentially with the size of the computing device. IBM has succeeded in building a first working quantum computing device with up to 7 qubits based on NMR technology, however, the construction of large multi-qubit systems appears to become extremely difficult due to the loss of coherence of the quantum states. Like the design process of modern microprocessors which is carried out by means of sophisticated software, modelling and simulation of the entire QC device is even more relevant. Simulation is required in order to understand the functioning of quantum algorithms, to construct novel quantum algorithms, to write quantum programs, to teach quantum computing, to construct real quantum computers, to understand and fight de-coherence and to understand and control the influence of the environment. Since quantum parallelism increases exponentially with the size of the quantum computer, parallel supercomputers are required for realistic simulations. I intend to give an introduction into the simulation of quantum computers using conventional computers. The simulation is based on a generic physical model of quantum computer hardware. Issues like parallel gate level simulators, modelling of QCs, simulators for physical quantum computers are addressed.

ARCS Workshops•Jan 1, 2004•0 citations
A simulator for quantum information systems cannot be both general, that is, easily used for every possible system, and efficient. Therefore, some systems will have aspects which can only be simulated by cunning modeling. On the other hand, a simulation may conveniently do extra-systemic processing that would be impractical in a real system. We illustrate with examples from our quantum computing simulator, QCSim. We model the [3,1] Hamming code in the presence of random bit flip or generalized amplitude damping noise, and calculate the expected result in one simulation run, as opposed to, say, a Monte Carlo simulation, and keep the original state to compute the chance of successful transmission, too. We also model the BB84 protocol with eavesdropping and random choice of basis and compute the chance of information received faithfully. Finally, we present our simulation of teleportation as an example of the trade-off between complexity of the simulation model and complexity of simulation inputs and as an example of modeling measurements and classical bits.
Quantum-mechanical phenomena are playing an increasing role in information processing as transistor sizes approach the nanometer level, while the securest forms of communication rely on quantum data encoding. When they involve a finite number of basis states, these phenomena can be modeled as quantum circuits, the quantum analogue of conventional or classical logic circuits. Simulation of quantum circuits can therefore be used as a tool to evaluate issues in the design of quantum information processors. Unfortunately, simulating such phenomena efficiently is exceedingly difficult. The matrices representing quantum operators (gates) and vectors modeling quantum states grow exponentially with the number of quantum bits. The information represented by quantum states and operators often exhibits structure that can be exploited when simulating certain classes of quantum circuits. We study the development of simulation methods that run on classical computers and take advantage of such repetitions and redundancies. In particular, we define a new data structure for simulating quantum circuits called the quantum information decision diagram (QuIDD). A QuIDD is a compressed graph representation of a vector or matrix and permits computations to be performed directly on the compressed data. We develop a comprehensive set of algorithms for operating on QuIDDs in both the state-vector and density-matrix formats, and evaluate their complexity. These algorithms have been implemented in a general-purpose simulator program for quantum-mechanical applications called QuIDDPro. Through extensive experiments conducted on representative quantum simulation applications, including Grover's search algorithm, error characterization, and reversible circuits, we demonstrate that QuIDDPro is faster than other existing quantum-mechanical simulators such as the National Institute of Standards and Technology's QCSim program, and is far more memory-efficient. Using QuIDDPro, we explore the advantages of quantum computation over classical computation, simulate quantum errors and error correction, and study the impact of numerical precision on the fidelity of simulations. We also develop several novel algorithms for testing quantum circuit equivalence and compare them empirically. The QuIDDPro software is equipped with a user-friendly interface and is distributed with numerous example scripts. It has been used as a laboratory supplement for quantum computing courses at several universities.
In general, all forms of information processing can be considered in a quantum mechanical context, including for example communication, channel capacities, and the quantum limits to information extraction. In this chapter we introduce the basic features of quantum information processing. We first present qubits as abstractions of two-level addressable quantum systems, before generalizing this concept to higher-dimensional qudit systems, and continuous variables. We introduce the stabilizer formalism towards the beginning of our discussion as a convenient way to track quantum information. In Section 2.2 we derive the no-cloning theorem, which leads us to cryptography, teleportation, and quantum repeaters. Section 2.3 describes quantum computing with qubits. We start with a brief description of the circuit model, and use it to define cluster states and the one-way model. We study the properties of cluster states and discuss error correction. In the last section we introduce quantum computing over continuous variables. Quantum information Classically, information is carried by ‘bits’, which are physical systems that have two (macroscopic) states denoted by 0 and 1. These bits are described classically, which immediately raises the question of how we should extend this information-theoretic description to the quantum mechanical case. This will lead to the quantum unit of information, the quantum bit or ‘qubit’. 2.1.1 Classical and quantum bits We can define the qubit as a two-dimensional quantum system, which means that the state space of the system is a two-dimensional complex Hilbert space ℋ.
Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation is a useful tool for determining the feasibility of quantum computers in the presence of errors. The size of a quantum computer that can be simulat ed is small because faithfully modeling a quantum computer requires an exponential amount of storage and number of operations. In this paper we define simulation models to study the feasibility of quantum computers. The most detailed of these models is based directly on a proposed imple mentation. We also define less detailed models which are exponentially less complex but still pro duce accurate results. Finally we show that the two different types of errors, decoherence and inaccuracies, are uncorrelated. This decreases the number of simulations which must be per formed.
The theory of quantum trajectories is applied to simulate the effects of quantum noise sources induced by the environment on quantum information protocols. We study two models that generalize single qubit noise channels like amplitude damping and phase flip to the many-qubit situation. We calculate the fidelity of quantum information transmission through a chaotic channel using the teleportation scheme with different environments. In this example, we analyze the role played by the kind of collective noise suffered by the quantum processor during its operation. We also investigate the stability of a quantum algorithm simulating the quantum dynamics of a paradigmatic model of chaos, the baker's map. Our results demonstrate that, using the quantum trajectories approach, we are able to simulate quantum protocols in the presence of noise and with large system sizes of more than 20 qubits.
Noise is a major challenge for current quantum computers. It can be broadly categorized into bit-flip and phase-flip errors. These two types do not necessarily affect the executed algorithm, thus also the application, in the same way. We illustrate this general effect for the example of the quantum approximate optimization algorithm (QAOA) applied to a small instance of the flight-gate assignment (FGA) problem. We compare bit-flip and phase-flip Pauli noise under both layer-level and gate-level noise models, using two circuit decompositions of the same ideal QAOA unitary: a CNOT-based decomposition and a native-RZZR_{ZZ}RZZ​ decomposition. In the simulations, bit-flip noise produces the larger degradation in the performance of the quantum optimization. The asymmetry is most visible in the layer-level and native-RZZR_{ZZ}RZZ​ simulations. We explain this by how the errors affect mixing, final measurements, and how they propagate inside the circuit. We then exploit these insights to tackle noise particularly efficiently using asymmetric error-correcting codes. As an illustration, we use the quantum parity code (QPC), a generalization of the 9-qubit Shor code, and show that a smaller asymmetric code can achieve nearly the same improvement as a larger symmetric choice. This demonstrates that error-correction resources should be assigned not only according to physical error rates, but also according to how strongly each error channel affects the application. As a result, asymmetric quantum error correction proves useful even in cases where the noise model is symmetric. Finally, we discuss how information about the noise obtained through calibration can be exploited in our approach.
Quantum computing is based on the exploitation of quantum effects to perform some important computations more efficiently than ever possible on classical computers. Well known quantum algorithms are Shors polynomial time factoring algorithm and Grovers data base search scheme. Their potential is due to the parallelism of a quantum computation increasing exponentially with the size of the computing device. IBM has succeeded in building a first working quantum computing device with up to 7 qubits based on NMR technology, however, the construction of large multi-qubit systems appears to become extremely difficult due to the loss of coherence of the quantum states. Like the design process of modern microprocessors which is carried out by means of sophisticated software, modelling and simulation of the entire QC device is even more relevant. Simulation is required in order to understand the functioning of quantum algorithms, to construct novel quantum algorithms, to write quantum programs, to teach quantum computing, to construct real quantum computers, to understand and fight de-coherence and to understand and control the influence of the environment. Since quantum parallelism increases exponentially with the size of the quantum computer, parallel supercomputers are required for realistic simulations. I intend to give an introduction into the simulation of quantum computers using conventional computers. The simulation is based on a generic physical model of quantum computer hardware. Issues like parallel gate level simulators, modelling of QCs, simulators for physical quantum computers are addressed.