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Simulating Noisy Quantum Circuits with Matrix Product Density Operators [article]

Song Cheng, Chenfeng Cao, Chao Zhang, Yongxiang Liu, Shi-Yao Hou, Pengxiang Xu, Bei Zeng
2020 arXiv   pre-print
In this work, we simulate random quantum circuits in 1D with Matrix Product Density Operators (MPDO), for different noise models such as dephasing, depolarizing, and amplitude damping.  ...  Compared with the method of Matrix Product Operators (MPO), the MPDO method reflects a clear physical picture of noise (with inner indices taking care of the noise simulation) and quantum entanglement  ...  In this work, we simulate noisy 1D random quantum circuits with Matrix Product Density Operators (MPDO), based on the MPDO construction proposed in [25] .  ... 
arXiv:2004.02388v3 fatcat:ivohpgbdhbc45cmyvpwwkdy6zi

Noisy induced entanglement transition in one-dimensional random quantum circuits [article]

Qi Zhang, Guang-Ming Zhang
2022 arXiv   pre-print
In this paper, we considered a one-dimensional quantum circuit with noisy Haar-random unitary gates using density matrix operator and tensor contraction methods.  ...  Random quantum circuit is a minimally structured model to study the entanglement dynamics of many-body quantum systems.  ...  In this paper, we considered a one-dimensional quantum circuit with noisy Haar-random unitary gates using density matrix operator and tensor contraction methods.  ... 
arXiv:2203.07791v2 fatcat:lgv6wd32ond3fpcelmxfm23thy

Psitrum: An Open Source Simulator for Universal Quantum Computers [article]

Mohammed Alghadeer and Eid Aldawsari and Raja Selvarajan and Khaled Alutaibi and Sabre Kais and Fahhad H Alharbi
2022 arXiv   pre-print
The simulator allows to emulate and debug quantum algorithms in form of quantum circuits for many applications with the choice of adding variety of noise modules to simulate decoherence in quantum circuits  ...  Simulators of universal quantum computer are important for understanding the basic principles and operations of the current noisy intermediate-scale quantum (NISQ) processors, and for building in future  ...  In such circuits, only matrix multiplication and tensor products are the advanced mathematical operations that are used.  ... 
arXiv:2203.07301v1 fatcat:5kl6tljqs5gbrkwudogtagzf4m

Limitations of Noisy Reversible Computation [article]

D. Aharonov and M. Ben-Or(CS,Hebrew univ.) and R. Impagliazzo
1996 arXiv   pre-print
In our noisy reversible circuits, each wire is flipped with probability p each time step, and all the inputs to the circuit are present in time 0.  ...  This establishes that noisy reversible computation has the power of the complexity class NC^1. We extend this to quantum circuits(QC).  ...  We next give a lower bound on the power of noisy quantum circuits: We show that noisy quantum circuits can simulate general quantum circuits, with an exponential cost.  ... 
arXiv:quant-ph/9611028v1 fatcat:eehjdujtuffk3n4bj4khaxxjwu

A Software Simulator for Noisy Quantum Circuits [article]

Himanshu Chaudhary, Biplab Mahato, Lakshya Priyadarshi, Naman Roshan, Utkarsh, Apoorva D. Patel
2021 arXiv   pre-print
We have developed a software library that simulates noisy quantum logic circuits.  ...  Our quantum simulator is implemented as a new backend on IBM's open-source Qiskit platform. In this document, we provide its description, and illustrate it with some simple examples.  ...  noisy quantum logic circuits.  ... 
arXiv:1908.05154v2 fatcat:yu5xjv2vw5b53mzxymjpwb7fsm

TQSim: A Case for Reuse-Focused Tree-Based Quantum Circuit Simulation [article]

Meng Wang, Rui Huang, Swamit Tannu, Prashant Nair
2022 arXiv   pre-print
To address this, we propose a noisy simulation technique called Tree-Based Quantum Circuit Simulation (TQSim).  ...  Unfortunately, noisy quantum simulators iteratively execute the same circuit across multiple trials (shots), thereby incurring high-performance overheads.  ...  Noisy Quantum Circuit Simulators: Taxonomy Broadly, there are two practical methods for performing noisy quantum circuit simulation. 1) Density Matrix Simulator: A Density Matrix can be used to represent  ... 
arXiv:2203.13892v1 fatcat:mp2tyqos2bgjblrl4kzpy6b3dq

Low Rank Density Matrix Evolution for Noisy Quantum Circuits [article]

Yi-Ting Chen, Collin Farquhar, Robert M. Parrish
2020 arXiv   pre-print
In this work, we present an efficient rank-compression approach for the classical simulation of Kraus decoherence channels in noisy quantum circuits.  ...  The approximation is achieved through iterative compression of the density matrix based on its leading eigenbasis during each simulation step without the need to store, manipulate, or diagonalize the full  ...  noisy quantum circuits.  ... 
arXiv:2009.06657v1 fatcat:ul2ctrwrvvbzrjninzohiszfqy

HybridQ: A Hybrid Simulator for Quantum Circuits [article]

Salvatore Mandrà, Jeffrey Marshall, Eleanor G. Rieffel, Rupak Biswas
2021 arXiv   pre-print
Developing state-of-the-art classical simulators of quantum circuits is of utmost importance to test and evaluate early quantum technology and understand the true potential of full-blown error-corrected  ...  The powerful tools of HybridQ allow users to manipulate, develop, and extend noiseless and noisy circuits for different hardware architectures.  ...  For instance, it is possible to compute expectation values of local operators of noisy circuits by using tensor contraction, without the need to simulate the full density matrix.  ... 
arXiv:2111.06868v1 fatcat:kc3jmbfqh5arbelxdacxrpwmpa

Low-rank density-matrix evolution for noisy quantum circuits

Yi-Ting Chen, Collin Farquhar, Robert M. Parrish
2021 npj Quantum Information  
AbstractIn this work, we present an efficient rank-compression approach for the classical simulation of Kraus decoherence channels in noisy quantum circuits.  ...  The approximation is achieved through iterative compression of the density matrix based on its leading eigenbasis during each simulation step without the need to store, manipulate, or diagonalize the full  ...  A density matrix, ρ, can always be decomposed as an outer product of the L 2 C 2 N V matrix, ρ LL y ; (2) for some V 2 N.  ... 
doi:10.1038/s41534-021-00392-4 fatcat:224x2omzzvgsbhcptabjufbgui

Gleipnir: Toward Practical Error Analysis for Quantum Programs (Extended Version) [article]

Runzhou Tao, Yunong Shi, Jianan Yao, John Hui, Frederic T. Chong, Ronghui Gu
2021 arXiv   pre-print
This predicate (ρ̂,δ) can be computed adaptively using tensor networks based on the Matrix Product States.  ...  Practical error analysis is essential for the design, optimization, and evaluation of Noisy Intermediate-Scale Quantum(NISQ) computing.  ...  density matrix space of dimension and is the space of linear operators.  ... 
arXiv:2104.06349v2 fatcat:sx2pch6zyzdvvgmbakoaflocm4

Recursive Variational Quantum Compiling [article]

Stian Bilek, Kristian Wold
2022 arXiv   pre-print
Variational quantum compiling algorithms aim to compress quantum circuits into parameterized ansatzes utilizing a hybrid quantum-classical approach.  ...  To show that this approach has an edge over the standard VQC method for sufficiently large circuit depths, RVQC was compared with VQC on a noise model of the IBM Santiago device with the goal of compressing  ...  A density matrix ρ with subscript A and R refers to the density matrix for the ansatz and random circuit, respectively.A density matrix ρ with superscript I and N implies that the density matrix is ideal  ... 
arXiv:2203.08514v1 fatcat:dtrkqckwivdvzee6kqojvqtpv4

Maximal entropy approach for quantum state tomography [article]

Rishabh Gupta, Rongxin Xia, Raphael D. Levine, Sabre Kais
2020 arXiv   pre-print
This can then be used to reconstruct the density matrix with high fidelity even though the results for some observables are missing.  ...  One of the most common ways of validation for an n-qubit quantum system is quantum tomography, which tries to reconstruct a quantum system's density matrix by a complete set of observables.  ...  To test the reconstruction of density matrix we first built various quantum circuits by applying different gate models followed by simulating the circuit with the Aer provider in Qiskit.  ... 
arXiv:2009.00815v2 fatcat:q5zuzvxvivbbfcmxni4tf4jvp4

Quantum error mitigation via matrix product operators [article]

Yuchen Guo, Shuo Yang
2022 arXiv   pre-print
Here, we introduce a QEM method based on the matrix product operator (MPO) representation of a quantum circuit that can characterize the noise channel with polynomial complexity.  ...  In the era of noisy intermediate-scale quantum (NISQ) devices, the number of controllable hardware qubits is insufficient to implement quantum error correction (QEC).  ...  -We introduce a variational technique to calculate the inverse of a noisy quantum circuit with matrix product operators.  ... 
arXiv:2201.00752v3 fatcat:ingljzhmrvalbbupekexp3todm

Efficient classical simulation of noisy random quantum circuits in one dimension [article]

Kyungjoo Noh, Liang Jiang, Bill Fefferman
2020 arXiv   pre-print
In particular, we simulate the real-time dynamics of 1D noisy random quantum circuits via matrix product operators (MPOs) and characterize the computational power of the 1D noisy quantum system by using  ...  Specifically, we study noisy random circuit sampling in one dimension (or 1D noisy RCS) as a simple model for exploring the effects of noise on the computational power of a noisy quantum device.  ...  More specifically, we directly simulate the mixed state dynamics of 1D noisy random quantum circuits by using matrix product operators (MPOs) [47, 48] .  ... 
arXiv:2003.13163v3 fatcat:7gd5f4wfyfeifhgfuyjo6vl5fi

Efficient classical simulation of noisy random quantum circuits in one dimension

Kyungjoo Noh, Liang Jiang, Bill Fefferman
2020 Quantum  
In particular, we simulate the real-time dynamics of 1D noisy random quantum circuits via matrix product operators (MPOs) and characterize the computational power of the 1D noisy quantum system by using  ...  Specifically, we study noisy random circuit sampling in one dimension (or 1D noisy RCS) as a simple model for exploring the effects of noise on the computational power of a noisy quantum device.  ...  More specifically, we directly simulate the mixed state dynamics of 1D noisy random quantum circuits by using matrix product operators (MPOs) [47, 48] .  ... 
doi:10.22331/q-2020-09-11-318 fatcat:iatkyffnqfbivf2ivaojmldmw4
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