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Finding Efficient Circuits for Ensemble Computation [chapter]

Matti Järvisalo, Petteri Kaski, Mikko Koivisto, Janne H. Korhonen
2012 Lecture Notes in Computer Science  
Furthermore, by developing a SAT encoding for the ensemble computation problem and by employing state-of-the-art SAT solvers, we search for concrete instances that would witness a substantial separation  ...  Given a Boolean function as input, a fundamental problem is to find a Boolean circuit with the least number of elementary gates (AND, OR, NOT) that computes the function.  ...  We thank Teppo Niinimäki for insight concerning the construction in Theorem 1.  ... 
doi:10.1007/978-3-642-31612-8_28 fatcat:vhihwttlfbg3tcey7rsbkl2nte

Estimating the frame potential of large-scale quantum circuit sampling using tensor networks up to 50 qubits [article]

Minzhao Liu, Junyu Liu, Yuri Alexeev, Liang Jiang
2022 arXiv   pre-print
Our tensor-network-based algorithm has polynomial complexity for shallow circuits and is high performing using CPU and GPU parallelism.  ...  We develop numerical protocols for estimating the frame potential, the 2-norm distance between a given ensemble and the exact Haar randomness, using the platform.  ...  We compute and store the individual trace values for each sampled circuit, and use the same trace values to compute frame potentials with different k values.  ... 
arXiv:2205.09900v1 fatcat:pcprbd6jijemrpax7p3xzfdq6m

Scalable and Flexible Classical Shadow Tomography with Tensor Networks [article]

Ahmed A. Akhtar, Hong-Ye Hu, Yi-Zhuang You
2022 arXiv   pre-print
The method combines the recently proposed locally-scrambled classical shadow tomography framework with tensor network techniques to achieve scalability for computing the classical shadow reconstruction  ...  The method enables classical shadow tomography to be performed on shallow quantum circuits with superior sample efficiency and minimal gate overhead and is friendly to noisy intermediate-scale quantum  ...  We thank Soonwon Choi for the helpful discussion and previous collaboration. We also thank Xun Gao for the helpful discussion on tensor networks.  ... 
arXiv:2209.02093v1 fatcat:sacg4kummrb73jp7obucekhzte

Derandomizing Quantum Circuits with Measurement-Based Unitary Designs

Peter S. Turner, Damian Markham
2016 Physical Review Letters  
Entangled multipartite states are resources for universal quantum computation, but they can also give rise to ensembles of unitary transformations, a topic usually studied in the context of random quantum  ...  circuits.  ...  Efficient random circuit constructions for generating approximate t designs have been shown [10] .  ... 
doi:10.1103/physrevlett.116.200501 pmid:27258858 fatcat:r544hbdiqrhidp6jhoxkn6achm

Quantum supremacy with spin squeezed atomic ensembles [article]

Yueheng Shi, Junheng Shi, Tim Byrnes
2022 arXiv   pre-print
The scheme can be implemented with hot or cold atomic ensembles.  ...  Each ensemble is assumed to be controllable only with its total spin.  ...  For ensemble sizes N = 10 12 and M = 2 such an exact computation is not tractable.  ... 
arXiv:2204.11772v1 fatcat:jonihamg6natpcjlv7ynvn5aym

Performance of the Quantum Approximate Optimization Algorithm on the Maximum Cut Problem [article]

Gavin E. Crooks
2018 arXiv   pre-print
The Quantum Approximate Optimization Algorithm (QAOA) is a promising approach for programming a near-term gate-based hybrid quantum computer to find good approximate solutions of hard combinatorial problems  ...  Moreover, MaxCut QAOA can be efficiently implemented on a gate-based quantum computer with limited qubit connectivity, using a qubit swap network.  ...  Acknowledgements -We heartily thank Matthew Harrigan, Jonathan Ward, Keri McKiernan, Chris Wilson, and Marcus da Silva for astute discussions.  ... 
arXiv:1811.08419v1 fatcat:4jlkfy2gtfbx7b44yasdtce4am

Boosting Quantum Fidelity with an Ordered Diverse Ensemble of Clifford Canary Circuits [article]

Gokul Subramanian Ravi, Jonathan M. Baker, Kaitlin N. Smith, Nathan Earnest, Ali Javadi-Abhari, Frederic Chong
2022 arXiv   pre-print
This paper aims to boost quantum fidelity with Clifford canary circuits by proposing Quancorde: Quantum Canary Ordered Diverse Ensembles, a fundamentally new approach to identifying the correct outcomes  ...  Quancorde utilizes Clifford canary circuits (which are classically simulable, but also resemble the target application structure and thus suffer similar structural noise impact) to order a diverse ensemble  ...  Canary circuits are efficiently constructed on classical compute.  ... 
arXiv:2209.13732v1 fatcat:3d7flndqqrdhpfusimsn4l2klm

Sparse pseudorandom distributions

Oded Goldreich, Hugo Krawczyk
1992 Random structures & algorithms (Print)  
Any polynomial-time algorithm trying to find a string in their support will succeed with negligible probability.  ...  Pseudorandom distributions on n-bit strings are ones which cannot be efficiently distinguished from the uniform distribution on strings of the same length.  ...  ACKNOWLEDGEMENTS We would like to thank Micha Hofri for referring us to Hoeffding inequality, and to Benny Chor and Eyal Kushilevitz for helpful comments.  ... 
doi:10.1002/rsa.3240030206 fatcat:cfywwwbbr5as5mcm7fm2lvai7y

Kernel-Function Based Quantum Algorithms for Finite Temperature Quantum Simulation [article]

Hai Wang, Jue Nan, Tao Zhang, Xingze Qiu, Wenlan Chen, Xiaopeng Li
2022 arXiv   pre-print
For quantum Hamiltonians, whose ground states are preparable with polynomial quantum circuits, THEI has an overall polynomial complexity.  ...  We demonstrate its efficiency with applications to one and two-dimensional quantum spin models, and a fermionic lattice.  ...  By writing the Fourier moments in the form of, c n = 1 D Re Tr e −inπ Ĥ , (3) we find these moments can be obtained efficiently by a quantum circuit shown in Fig. 1 (a), which contains L number of physical  ... 
arXiv:2202.01170v2 fatcat:czou2bdhrzec3haie27hidee44

On the Relationship Between Probabilistic Circuits and Determinantal Point Processes [article]

Honghua Zhang, Steven Holtzen, Guy Van den Broeck
2020 arXiv   pre-print
We propose a unified analysis and shared language for discussing DPPs and PCs.  ...  Central to this effort is the development of tractable probabilistic models (TPMs): models whose structure guarantees efficient probabilistic inference algorithms.  ...  In particular, we thank Richard Elman for detailed and insightful discussion on algebra.  ... 
arXiv:2006.15233v1 fatcat:xhoyhkugandn3bl6u5bjrm3jaq

Page 5255 of Mathematical Reviews Vol. , Issue 98H [page]

1998 Mathematical Reviews  
., sub-polynomial), this ensemble can be dis- tinguished from the uniform ensemble by a (non-uniform) family of small circuits.  ...  {For the entire collection see MR 98c:68007. } 98h:68086 68Q15 68Q05 Goldreich, Oded (IL-WEIZ-AC; Rehovot); Meyer, Bernd |Meyer, Bernd’ | Computational indistinguishability: algorithms vs. circuits.  ... 

On the (Im)possibility of Obfuscating Programs [chapter]

Boaz Barak, Oded Goldreich, Rusell Impagliazzo, Steven Rudich, Amit Sahai, Salil Vadhan, Ke Yang
2001 Lecture Notes in Computer Science  
compute given O(P ), one could also efficiently compute given oracle access to P .  ...  only need to work for very restricted models of computation (TC 0 ).  ...  Further support for this work was provided to Boaz Barak  ... 
doi:10.1007/3-540-44647-8_1 fatcat:z5p3cubaxrd5lp3bysrxuamxhi

Computing Free Energies with Fluctuation Relations on Quantum Computers [article]

Lindsay Bassman, Katherine Klymko, Diyi Liu, Norman M. Tubman, Wibe A. de Jong
2021 arXiv   pre-print
Fluctuation relations allow for the computation of equilibrium properties, like free energy, from an ensemble of non-equilibrium dynamics simulations.  ...  Quantum computers can alleviate this hurdle, as they can efficiently simulate quantum systems.  ...  One potential path forward for computing this ensemble of trajectories is to employ quantum computers, which can efficiently simulate the dynamics of quantum systems [32] [33] [34] [35] .  ... 
arXiv:2103.09846v2 fatcat:tb3syrasjre27nylkrd22ifzde

Strudel: Learning Structured-Decomposable Probabilistic Circuits [article]

Meihua Dang, Antonio Vergari, Guy Van den Broeck
2020 arXiv   pre-print
Probabilistic circuits (PCs) represent a probability distribution as a computational graph.  ...  Compared to prior work for learning structured-decomposable PCs, Strudel delivers more accurate single PC models in fewer iterations, and dramatically scales learning when building ensembles of PCs.  ...  Table 1 : Circuit flows for fast inference of ensembles for each dataset.  ... 
arXiv:2007.09331v2 fatcat:yzfyh4jpfrdyjpnliapxmw5w3i

On Round-Efficient Argument Systems [chapter]

Hoeteck Wee
2005 Lecture Notes in Computer Science  
We consider the problem of constructing round-efficient public-coin argument systems, that is, interactive proof systems that are only computationally sound with a constant number of rounds.  ...  Finally, we show that the Fiat-Shamir paradigm [FS86] and Babai-Moran round reduction [BM88] fails to preserve computational soundness for some 3-round and 4-round argument systems.  ...  with an efficiently computable function ensemble yields an insecure signature scheme.  ... 
doi:10.1007/11523468_12 fatcat:x3k2vjcelzct5oggyjy2kujd3y
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