@article{Luo2020,
	title = {Yao.jl: {Extensible}, {Efficient} {Framework} for {Quantum} {Algorithm} {Design}},
	volume = {4},
	shorttitle = {Yao.jl},
	url = {https://quantum-journal.org/papers/q-2020-10-11-341/},
	doi = {10.22331/q-2020-10-11-341},
	abstract = {Xiu-Zhe Luo, Jin-Guo Liu, Pan Zhang, and Lei Wang,
Quantum 4, 341 (2020).
We introduce \${\textbackslash}texttt\{Yao\}\$, an extensible, efficient open-source framework for quantum algorithm design. \${\textbackslash}texttt\{Yao\}\$ features generic and differentiable programming of quantum circuits. It a…},
	language = {en-GB},
	urldate = {2023-03-23},
	journal = {Quantum},
	author = {Luo, Xiu-Zhe and Liu, Jin-Guo and Zhang, Pan and Wang, Lei},
	month = oct,
	year = {2020},
	note = {Publisher: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften},
	pages = {341},
}

@article{Pan2022,
	title = {Simulation of {Quantum} {Circuits} {Using} the {Big}-{Batch} {Tensor} {Network} {Method}},
	volume = {128},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.128.030501},
	doi = {10.1103/PhysRevLett.128.030501},
	abstract = {We propose a tensor network approach to compute amplitudes and probabilities for a large number of correlated bitstrings in the final state of a quantum circuit. As an application, we study Google’s Sycamore circuits, which are believed to be beyond the reach of classical supercomputers and have been used to demonstrate quantum supremacy. By employing a small computational cluster containing 60 graphical processing units (GPUs), we compute exact amplitudes and probabilities of 2×106 correlated bitstrings with some entries fixed (which span a subspace of the output probability distribution) for the Sycamore circuit with 53 qubits and 20 cycles. The obtained results verify the Porter-Thomas distribution of the large and deep quantum circuits of Google, provide datasets and benchmarks for developing approximate simulation methods, and can be used for spoofing the linear cross entropy benchmark of quantum supremacy. Then we extend the proposed big-batch method to a full-amplitude simulation approach that is more efficient than the existing Schrödinger method on shallow circuits and the Schrödinger-Feynman method in general, enabling us to obtain the state vector of Google’s simplifiable circuit with n=43 qubits and m=14 cycles using only one GPU. We also manage to obtain the state vector for Google’s simplifiable circuits with n=50 qubits and m=14 cycles using a small GPU cluster, breaking the previous record on the number of qubits in full-amplitude simulations. Our method is general in computing bitstring probabilities for a broad class of quantum circuits and can find applications in the verification of quantum computers. We anticipate that our method will pave the way for combining tensor network–based classical computations and near-term quantum computations for solving challenging problems in the real world.},
	number = {3},
	urldate = {2023-02-09},
	journal = {Physical Review Letters},
	author = {Pan, Feng and Zhang, Pan},
	month = jan,
	year = {2022},
	note = {Publisher: American Physical Society},
	pages = {030501},
}

@article{Kalachev2021,
	title = {Recursive {Multi}-{Tensor} {Contraction} for {XEB} {Verification} of {Quantum} {Circuits}},
	url = {http://arxiv.org/abs/2108.05665},
	abstract = {The computational advantage of noisy quantum computers have been demonstrated by sampling the bitstrings of quantum random circuits. An important issue is how the performance of quantum devices could be quantified in the so-called "supremacy regime". The standard approach is through the linear cross entropy (XEB), where the theoretical value of the probability is required for each bitstring. However, the computational cost of XEB grows exponentially. So far, random circuits of the 53-qubit Sycamore chip was verified up to 10 cycles of gates only; the XEB fidelities of deeper circuits were approximated with simplified circuits instead. Here we present a multi-tensor contraction algorithm for speeding up the calculations of XEB of quantum circuits, where the computational cost can be significantly reduced through a recursive manner with some form of memoization. As a demonstration, we analyzed the experimental data of the 53-qubit Sycamore chip and obtained the exact values of the corresponding XEB fidelities up to 16 cycles using only moderate computing resources (few GPUs). If the algorithm was implemented on the Summit supercomputer, we estimate that for the 20-cycles supremacy circuits, it would only cost 7.5 days, which is several orders of magnitudes lower than previously estimated in the literature.},
	author = {Kalachev, Gleb and Panteleev, Pavel and Yung, Man-Hong},
	year = {2021},
	note = {arXiv: 2108.05665},
	pages = {1--9},
}

@article{Markov2008,
	title = {Simulating {Quantum} {Computation} by {Contracting} {Tensor} {Networks}},
	volume = {38},
	issn = {0097-5397},
	url = {https://epubs.siam.org/doi/abs/10.1137/050644756},
	doi = {10.1137/050644756},
	abstract = {Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power was unknown. We describe an efficient adiabatic simulation of any given quantum algorithm, which implies that the adiabatic computation model and the conventional quantum computation model are polynomially equivalent. Our result can be extended to the physically realistic setting of particles arranged on a two‐dimensional grid with nearest neighbor interactions. The equivalence between the models allows stating the main open problems in quantum computation using well‐studied mathematical objects such as eigenvectors and spectral gaps of sparse matrices.},
	number = {3},
	urldate = {2023-10-05},
	journal = {SIAM Journal on Computing},
	author = {Markov, Igor L. and Shi, Yaoyun},
	month = jan,
	year = {2008},
	note = {Publisher: Society for Industrial and Applied Mathematics},
	pages = {963--981},
}
