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Permutational Quantum Computing [article]

Stephen P. Jordan
2009 arXiv   pre-print
Whereas topological quantum computation requires anyons, permutational quantum computation can be performed with ordinary spin-1/2 particles, using a variant of the spin-network scheme of Marzuoli and  ...  Nevertheless, permutational quantum computers can in polynomial time approximate matrix elements of certain irreducible representations of the symmetric group and simulate certain processes in the Ponzano-Regge  ...  Permutational computers can be simulated efficiently by standard quantum computers. Thus PQP is contained in BQP.  ... 
arXiv:0906.2508v1 fatcat:jixgqw2gnreyzagsmuw2dlc5om

Faster quantum computation with permutations and resonant couplings [article]

Yingkai Ouyang and Yi Shen and Lin Chen
2019 arXiv   pre-print
To achieve this, we perform certain single-qubit quantum computations by simply permuting the underlying qubits.  ...  Together with exchange-interactions or Ising-interactions and other resonant couplings, we present a new scheme for quantum computation that potentially improves the speed in which a quantum computation  ...  YO also acknowledges the support of the QCDA project which has received funding from the QuantERA ERANET Cofund in Quantum Technologies implemented within the European Unions Horizon 2020 Programme.  ... 
arXiv:1901.00252v4 fatcat:ysbzlhbmj5e7xjwynrgsbnixz4

Permutation groups, minimal degrees and quantum computing

Julia Kempe, László Pyber, Aner Shalev
2007 Groups, Geometry, and Dynamics  
A main application of our results concerns the Hidden Subgroup Problem for S n in quantum computing.  ...  We study permutation groups of given minimal degree without the classical primitivity assumption.  ...  The Hidden Subgroup Problem plays a central role in quantum computing.  ... 
doi:10.4171/ggd/24 fatcat:bhe56se7szbszbhjkgj6bbfhwy

Permutation groups, minimal degrees and quantum computing [article]

Julia Kempe, Laszlo Pyber, Aner Shalev
2006 arXiv   pre-print
A main application of our results concerns the Hidden Subgroup Problem for the symmetric group in Quantum Computing.  ...  We study permutation groups of given minimal degree without the classical primitivity assumption.  ...  The Hidden Subgroup Problem plays a central role in Quantum Computing.  ... 
arXiv:quant-ph/0607204v1 fatcat:fayrgb2mk5esraqwtukqxs2oiq

The Magic of Universal Quantum Computing with Permutations

Michel Planat, Rukhsan Ul Haq
2017 Advances in Mathematical Physics  
The role of permutation gates for universal quantum computing is investigated.  ...  The "magic" of computation is clarified in the permutation gates, their eigenstates, the Wootters discrete Wigner function, and state-dependent contextuality (following many contributions on this subject  ...  universality and efficiency of quantum computation.  ... 
doi:10.1155/2017/5287862 fatcat:7td34h5horgg3l4wez7ibnvnwm

Universal test for quantum one-way permutations

Akinori Kawachi, Hirotada Kobayashi, Takeshi Koshiba, Raymond H. Putra
2005 Theoretical Computer Science  
In the quantum computation model, Kashefi, Nishimura and Vedral gave a sufficient condition of (cryptographic) quantum one-way permutations and conjectured that the condition would be necessary.  ...  In this paper, we affirmatively settle their conjecture and complete a necessary and sufficient for quantum one-way permutations.  ...  Let f be a permutation that can be computed by a polynomial-size quantum circuit.  ... 
doi:10.1016/j.tcs.2005.07.036 fatcat:wl24pbwg75hnbiqp5adhe5muua

Quantum computation with charge-color permuting twists in qudit color codes [article]

Manoj G. Gowda, Pradeep Kiran Sarvepalli
2021 arXiv   pre-print
Twists are defects in the lattice which can be utilized to perform computations on encoded data.  ...  Making use of the construction, we give protocols to implement generalized Clifford gates using charge-color permuting twists.  ...  They were proposed with a view to enable transversal quantum gates providing a route to fault tolerant quantum computation.  ... 
arXiv:2110.08680v1 fatcat:e4zp27k3gjbunflvwcx5vwyhqe

Quantum Circuits for the Unitary Permutation Problem [chapter]

Stefano Facchini, Simon Perdrix
2015 Lecture Notes in Computer Science  
This problem has been introduced and investigated by Colnaghi et al. where two models of computations are considered.  ...  The upper and lower bounds for the standard quantum circuit model are established by pointing out connections with the permutation as substring problem introduced by Karp.  ...  To point out a separation between the standard model of quantum circuits and the quantum switch model, Colnaghi et al.  ... 
doi:10.1007/978-3-319-17142-5_28 fatcat:6a3m33uku5gcrbrkfsvybtcmvy

Recursive Methods for Synthesizing Permutations on Limited-Connectivity Quantum Computers [article]

Cynthia Chen, Bruno Schmitt, Helena Zhang, Lev S. Bishop, Ali Javadi-Abhari
2022 arXiv   pre-print
We describe a family of recursive methods for the synthesis of qubit permutations on quantum computers with limited qubit connectivity. Two objectives are of importance: circuit size and depth.  ...  We demonstrate the utility of these algorithms by optimizing the compilation of Quantum Volume circuits, and to disprove an old conjecture on reversals being the hardest permutation on a path.  ...  Quantum Volume (QV) is a holistic metric for benchmarking quantum computers [7] .  ... 
arXiv:2207.06199v1 fatcat:wgzrh6b6avd6hndsbprpemz7e4

Quantum Bit-commitment for small storage based on quantum one-way permutations

Keisuke Tanaka
2003 New generation computing  
We propose quantum bit-commitment schemes based on quantum one-way permutations.  ...  Our future work is replacing assumption to quantum one-way functions from quantum one-way permutations.  ...  This does not exclude the study on quantum bit-commitment based on some quantum computational assumption.  ... 
doi:10.1007/bf03037308 fatcat:wdl2sqqd3bdc7bjbawnnyqnqom

Quantum Queries on Permutations [chapter]

Taisia Mischenko-Slatenkova, Alina Vasilieva, Ilja Kucevalovs, Rūsiņš Freivalds
2015 Lecture Notes in Computer Science  
Since then several authors have compared quantum and deterministic query algorithms for permutations. It turns out that the case of n-permutations where n is an odd number is difficult.  ...  Even for (2m)-permutations with m ≥ 2 the best proved advantage of quantum query algorithms is the result in [11] where the quantum query complexity is m but the deterministic query complexity is (2m−1  ...  It was proved that for 2m-permutations it suffices to have m quantum queries but for 2m + 1-permutations it suffices to have m + 1 quantum queries.  ... 
doi:10.1007/978-3-319-19225-3_15 fatcat:putn5hhe7fbjfnedv54v5bixum

Perfectly Concealing Quantum Bit Commitment from any Quantum One-Way Permutation [chapter]

Paul Dumais, Dominic Mayers, Louis Salvail
2000 Lecture Notes in Computer Science  
We show that although unconditionally secure quantum bit commitment is impossible, it can be based upon any family of quantum one-way permutations.  ...  Mayers [13] has proven that any quantum bit commitment scheme can either be defeated by the committer or the receiver as long as both sides have unrestricted quantum computational power.  ...  If a candidate family of quantum one-way functions was also computable efficiently on a classical computer then classical cryptography could provide computational security even against quantum adversaries  ... 
doi:10.1007/3-540-45539-6_21 fatcat:rwvkk6beqjayvkzpajbpfipin4

Quantum Queries on Permutations with a Promise [chapter]

Rūsiņš Freivalds, Kazuo Iwama
2009 Lecture Notes in Computer Science  
This paper studies quantum query complexities for deciding (exactly or with probability 1.0) the parity of permutations of n numbers, 0 through n−1.  ...  (iii) Our third result is for the problem deciding whether the given permutation is the identical one.  ...  In the case when the second half is asked the algorithm computes whether the second half of the permutation is even or odd.  ... 
doi:10.1007/978-3-642-02979-0_24 fatcat:ipkdmwyc7bff5m5yctwuuludc4

Universal Test for Quantum One-Way Permutations [chapter]

Akinori Kawachi, Hirotada Kobayashi, Takeshi Koshiba, Raymond H. Putra
2004 Lecture Notes in Computer Science  
In the quantum computation model, Kashefi, Nishimura and Vedral gave a sufficient condition of (cryptographic) quantum one-way permutations and conjectured that the condition would be necessary.  ...  In this paper, we affirmatively settle their conjecture and complete a necessary and sufficient for quantum one-way permutations.  ...  Theorem 3.2 Let f be a permutation that can be computed by a polynomial-size quantum circuit.  ... 
doi:10.1007/978-3-540-28629-5_66 fatcat:u42c2etzcba6ljho3rbwgglcgu

Quantum Permutation Synchronization

Tolga Birdal, Vladislav Golyanik, Christian Theobalt, Leonidas Guibas
2021 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)  
Hence, we: (i) show how to insert permutation constraints into a QUBO problem and (ii) solve the constrained QUBO problem on the current generation of the adiabatic quantum computers D-Wave.  ...  We present QuantumSync, the first quantum algorithm for solving a synchronization problem in the context of computer vision.  ...  The important cues are the correspondences denoting permutations, whose rows might be randomly swapped to inject noise. [29] Dataset description.  ... 
doi:10.1109/cvpr46437.2021.01292 fatcat:homzpo4abfaq7cqhxyhyu6surm
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