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We analyze the complexity of learning $n$-qubit quantum phase states.
Bounds for the quantity of information transmitted by a quantum communication channel
Alexander Semenovich Holevo · 1973
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The theory of error correcting codes
Florence Jessie MacWilliams and Neil James Alexander Sloane · 1977
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On the degree of Boolean functions as real polynomials
Noam Nisan and Mario Szegedy · 1994
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Quantum complexity theory
Ethan Bernstein and Umesh Vazirani · 1997
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Prescription for experimental determination of the dynamics of a quantum black box
Isaac L Chuang and Michael A Nielsen · 1997
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Spectral analysis of Boolean functions as a graph eigenvalue problem
A. Bernasconi and B. Codenotti · 1999
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Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations
Daniel Gottesman and Isaac L Chuang · 1999
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On quantum detection and the square-root measurement
Yonina C Eldar and G David Forney · 2001
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Reversing quantum dynamics with near-optimal quantum and classical fidelity
Howard Barnum and Emanuel Knill · 2002
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Stabilizer codes can be realized as graph codes
Dirk Schlingemann · 2002
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Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
Jeroen Dehaene and Bart De Moor · 2003
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Multiparty entanglement in graph states
Marc Hein, Jens Eisert, and Hans J Briegel · 2004
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Optimal measurements for the dihedral hidden subgroup problem
Dave Bacon, Andrew M Childs, and Wim van Dam · 2005
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The parity problem in the presence of noise, decoding random linear codes, and the subset sum problem
Vadim Lyubashevsky · 2005
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On the distinguishability of random quantum states
Ashley Montanaro · 2007
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Quantum-process tomography: Resource analysis of different strategies
Masoud Mohseni, Ali T Rezakhani, and Daniel A Lidar · 2008
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Semi-Clifford operations, structure of 𝒞 k {\mathcal{C}}_{k} hierarchy, and gate complexity for fault-tolerant quantum computation
Bei Zeng, Xie Chen, and Isaac L. Chuang · 2008
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Compressed sensing over finite fields
Stark C. Draper and Sheida Malekpour · 2009
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Learning and testing algorithms for the Clifford group
Richard A Low · 2009
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Quantum algorithms to solve the hidden shift problem for quadratics and for functions of large Gowers norm
Martin Rötteler · 2009
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Efficient quantum state tomography
Marcus Cramer, Martin B Plenio, Steven T Flammia, Rolando Somma, David Gross, Stephen D Bartlett, Olivier Landon-Cardinal, David Poulin, and Yi-Kai Liu · 2010
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Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
Michael J Bremner, Richard Jozsa, and Dan J Shepherd · 2011
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How many copies are needed for state discrimination?
Aram W Harrow and Andreas Winter · 2012
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The quantum query complexity of learning multilinear polynomials
Ashley Montanaro · 2012
Stabiliser states are efficiently PAC-Learnable
Andrea Rocchetto · 2018
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Simulation of quantum circuits by low-rank stabilizer decompositions
Sergey Bravyi, Dan Browne, Padraic Calpin, Earl Campbell, David Gosset, and Mark Howard · 2019
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(Pseudo) Random Quantum States with Binary Phase
Zvika Brakerski and Omri Shmueli · 2019
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Pretty simple bounds on quantum state discrimination
Ashley Montanaro · 2019
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Experimental learning of quantum states
Andrea Rocchetto, Scott Aaronson, Simone Severini, Gonzalo Carvacho, Davide Poderini, Iris Agresti, Marco Bentivegna, and Fabio Sciarrino · 2019
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Quantum computational universality of hypergraph states with Pauli-X and Z basis measurements
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Quantum hypergraph states
Matteo Rossi, Marcus Huber, Dagmar Bruß, and Chiara Macchiavello · 2013
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Analysis of Boolean Functions
Ryan O’Donnell · 2014
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Reed-Muller Codes for Random Erasures and Errors
Emmanuel Abbe, Amir Shpilka, and Avi Wigderson · 2015
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Improved classical simulation of quantum circuits dominated by Clifford gates
Sergey Bravyi and David Gosset · 2016
Cited alongside, same era.
Average-case complexity versus approximate simulation of commuting quantum computations
Michael J Bremner, Ashley Montanaro, and Dan J Shepherd · 2016
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Efficient quantum tomography
Ryan O’Donnell and John Wright · 2016
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Yuki Takeuchi, Tomoyuki Morimae, and Masahito Hayashi · 2019
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Reed–Muller Codes: Theory and Algorithms
Emmanuel Abbe, Amir Shpilka, and Min Ye · 2020
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Sample-efficient learning of interacting quantum systems
Anurag Anshu, Srinivasan Arunachalam, Tomotaka Kuwahara, and Mehdi Soleimanifar · 2021
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Cryptography from pseudorandom quantum states
Prabhanjan Ananth, Luowen Qian, and Henry Yuen · 2021
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Schur–Weyl duality for the Clifford group with applications: Property testing, a robust Hudson theorem, and de Finetti representations
David Gross, Sepehr Nezami, and Michael Walter · 2021
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Optimal learning of quantum Hamiltonians from high-temperature Gibbs states
Jeongwan Haah, Robin Kothari, and Ewin Tang · 2021
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Quantum search-to-decision reductions and the state synthesis problem
Sandy Irani, Anand Natarajan, Chinmay Nirkhe, Sujit Rao, and Henry Yuen · 2021
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Quantum advantage from energy measurements of many-body quantum systems
Leonardo Novo, Juani Bermejo-Vega, and Raúl García-Patrón · 2021
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Quantum tomography using state-preparation unitaries, 2022
Apeldoorn van Joran, Arjan Cornelissen, Andras Gilyén, and Giacomo Nannicini · 2022
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Learning quantum circuits of some T gates
Ching-Yi Lai and Hao-Chung Cheng · 2022
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Clifford Circuits can be Properly PAC Learned if and only if RP = NP \textsf{RP}=\textsf{NP}
Daniel Liang · 2022
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An improved sample complexity lower bound for quantum state tomography
Henry Yuen · 2022
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