9 Search Results for "Reichardt, Ben W."

Document
DOI: 10.4230/LIPIcs.ITCS.2026.26
Local Transformations of Bipartite Entanglement Are Rigid

Authors: John Bostanci, Tony Metger, and Henry Yuen

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
Uhlmann’s theorem is a fundamental result in quantum information theory that quantifies the optimal overlap between two bipartite pure states after applying local unitary operations (called Uhlmann transformations). We show that optimal Uhlmann transformations are rigid - in other words, they must be unique up to some well-characterized degrees of freedom. This rigidity is also robust: Uhlmann transformations achieving near-optimal overlaps must be close to the unique optimal transformation (again, up to well-characterized degrees of freedom). We describe two applications of our robust rigidity theorem: (a) we obtain better interactive proofs for synthesizing Uhlmann transformations and (b) we obtain a simple, alternative proof of the Gowers-Hatami theorem on the stability of approximate representations of finite groups.
Cite as

John Bostanci, Tony Metger, and Henry Yuen. Local Transformations of Bipartite Entanglement Are Rigid. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 26:1-26:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bostanci_et_al:LIPIcs.ITCS.2026.26,
  author =	{Bostanci, John and Metger, Tony and Yuen, Henry},
  title =	{{Local Transformations of Bipartite Entanglement Are Rigid}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{26:1--26:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.26},
  URN =		{urn:nbn:de:0030-drops-253138},
  doi =		{10.4230/LIPIcs.ITCS.2026.26},
  annote =	{Keywords: Uhlmann’s theorem, quantum entanglement, stability theorems}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.109
Cloning Games, Black Holes and Cryptography

Authors: Alexander Poremba, Seyoon Ragavan, and Vinod Vaikuntanathan

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
In this work, we introduce a new toolkit for analyzing cloning games, a notion that captures stronger and more quantitative versions of the celebrated quantum no-cloning theorem. This framework allows us to analyze a new cloning game based on binary phase states. Our results provide evidence that these games may be able to overcome important limitations of previous candidates based on BB84 states and subspace coset states: in a model where the adversaries are restricted to making a single oracle query, we show that the binary phase variant is t-copy secure when t = o(n/log n). Moreover, for constant t, we obtain the first optimal bounds of O(2^{-n}), asymptotically matching the value attained by a trivial adversarial strategy. We also show a worst-case to average-case reduction which allows us to show the same quantitative results for the new and natural notion of Haar cloning games. Our analytic toolkit, which we believe will find further applications, is based on binary subtypes and uses novel bounds on the operator norms of block-wise tensor products of matrices. To illustrate the effectiveness of these new techniques, we present two applications: first, in black-hole physics, where our asymptotically optimal bound offers quantitative insights into information scrambling in idealized models of black holes; and second, in unclonable cryptography, where we (a) construct succinct unclonable encryption schemes from the existence of pseudorandom unitaries, and (b) propose and provide evidence for the security of multi-copy unclonable encryption schemes.
Cite as

Alexander Poremba, Seyoon Ragavan, and Vinod Vaikuntanathan. Cloning Games, Black Holes and Cryptography. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 109:1-109:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{poremba_et_al:LIPIcs.ITCS.2026.109,
  author =	{Poremba, Alexander and Ragavan, Seyoon and Vaikuntanathan, Vinod},
  title =	{{Cloning Games, Black Holes and Cryptography}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{109:1--109:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.109},
  URN =		{urn:nbn:de:0030-drops-253961},
  doi =		{10.4230/LIPIcs.ITCS.2026.109},
  annote =	{Keywords: Unclonable cryptography, quantum pseudorandomness, black hole physics}
}
Document
DOI: 10.4230/LIPIcs.TQC.2025.9
Efficient Quantum Pseudorandomness from Hamiltonian Phase States

Authors: John Bostanci, Jonas Haferkamp, Dominik Hangleiter, and Alexander Poremba

Published in: LIPIcs, Volume 350, 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)

Abstract
Quantum pseudorandomness has found applications in many areas of quantum information, ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum systems, and, more recently, in the foundations of quantum cryptography. Kretschmer (TQC '21) showed that both pseudorandom states and pseudorandom unitaries exist even in a world without classical one-way functions. To this day, however, all known constructions require classical cryptographic building blocks which are themselves synonymous with the existence of one-way functions, and which are also challenging to implement on realistic quantum hardware. In this work, we seek to make progress on both of these fronts simultaneously - by decoupling quantum pseudorandomness from classical cryptography altogether. We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem, which is the task of decoding output states of a random instantaneous quantum polynomial-time (IQP) circuit. Hamiltonian phase states can be generated very efficiently using only Hadamard gates, single-qubit Z rotations and CNOT circuits. We show that the hardness of our problem reduces to a worst-case version of the problem, and we provide evidence that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions. We also show information-theoretic hardness when only few copies of HPS are available by proving an approximate t-design property of our ensemble. Finally, we show that our HPS assumption and its variants allow us to efficiently construct many pseudorandom quantum primitives, ranging from pseudorandom states, to quantum pseudoentanglement, to pseudorandom unitaries, and even primitives such as public-key encryption with quantum keys.
Cite as

John Bostanci, Jonas Haferkamp, Dominik Hangleiter, and Alexander Poremba. Efficient Quantum Pseudorandomness from Hamiltonian Phase States. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bostanci_et_al:LIPIcs.TQC.2025.9,
  author =	{Bostanci, John and Haferkamp, Jonas and Hangleiter, Dominik and Poremba, Alexander},
  title =	{{Efficient Quantum Pseudorandomness from Hamiltonian Phase States}},
  booktitle =	{20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-392-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{350},
  editor =	{Fefferman, Bill},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2025.9},
  URN =		{urn:nbn:de:0030-drops-240586},
  doi =		{10.4230/LIPIcs.TQC.2025.9},
  annote =	{Keywords: Quantum pseudorandomness, quantum phase states, quantum cryptography}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.38
An Algorithm for Tambara-Yamagami Quantum Invariants of 3-Manifolds, Parameterized by the First Betti Number

Authors: Colleen Delaney, Clément Maria, and Eric Samperton

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Quantum topology provides various frameworks for defining and computing invariants of manifolds inspired by quantum theory. One such framework of substantial interest in both mathematics and physics is the Turaev-Viro-Barrett-Westbury state sum construction, which uses the data of a spherical fusion category to define topological invariants of triangulated 3-manifolds via tensor network contractions. In this work we analyze the computational complexity of state sum invariants of 3-manifolds derived from Tambara-Yamagami categories. While these categories are the simplest source of state sum invariants beyond finite abelian groups (whose invariants can be computed in polynomial time) their computational complexities are yet to be fully understood. We first establish that the invariants arising from even the smallest Tambara-Yamagami categories are #P-hard to compute, so that one expects the same to be true of the whole family. Our main result is then the existence of a fixed parameter tractable algorithm to compute these 3-manifold invariants, where the parameter is the first Betti number of the 3-manifold with ℤ/2ℤ coefficients. Contrary to other domains of computational topology, such as graphs on surfaces, very few hard problems in 3-manifold topology are known to admit FPT algorithms with a topological parameter. However, such algorithms are of particular interest as their complexity depends only polynomially on the combinatorial representation of the input, regardless of size or combinatorial width. Additionally, in the case of Betti numbers, the parameter itself is computable in polynomial time. Thus while one generally expects quantum invariants to be hard to compute classically, our results suggest that the hardness of computing state sum invariants from Tambara-Yamagami categories arises from classical 3-manifold topology rather than the quantum nature of the algebraic input.
Cite as

Colleen Delaney, Clément Maria, and Eric Samperton. An Algorithm for Tambara-Yamagami Quantum Invariants of 3-Manifolds, Parameterized by the First Betti Number. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 38:1-38:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{delaney_et_al:LIPIcs.SoCG.2025.38,
  author =	{Delaney, Colleen and Maria, Cl\'{e}ment and Samperton, Eric},
  title =	{{An Algorithm for Tambara-Yamagami Quantum Invariants of 3-Manifolds, Parameterized by the First Betti Number}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{38:1--38:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.38},
  URN =		{urn:nbn:de:0030-drops-231901},
  doi =		{10.4230/LIPIcs.SoCG.2025.38},
  annote =	{Keywords: 3-manifold, quantum invariant, fixed parameter tractable algorithm, topological parameter, Gauss sums, topological quantum field theory}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.54
Multidimensional Quantum Walks, Recursion, and Quantum Divide & Conquer

Authors: Stacey Jeffery and Galina Pass

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We introduce an object called a subspace graph that formalizes the technique of multidimensional quantum walks. Composing subspace graphs allows one to seamlessly combine quantum and classical reasoning, keeping a classical structure in mind, while abstracting quantum parts into subgraphs with simple boundaries as needed. As an example, we show how to combine a switching network with arbitrary quantum subroutines, to compute a composed function. As another application, we give a time-efficient implementation of quantum Divide & Conquer when the sub-problems are combined via a Boolean formula. We use this to quadratically speed up Savitch’s algorithm for directed st-connectivity.
Cite as

Stacey Jeffery and Galina Pass. Multidimensional Quantum Walks, Recursion, and Quantum Divide & Conquer. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 54:1-54:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jeffery_et_al:LIPIcs.STACS.2025.54,
  author =	{Jeffery, Stacey and Pass, Galina},
  title =	{{Multidimensional Quantum Walks, Recursion, and Quantum Divide \& Conquer}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{54:1--54:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.54},
  URN =		{urn:nbn:de:0030-drops-228791},
  doi =		{10.4230/LIPIcs.STACS.2025.54},
  annote =	{Keywords: Quantum Divide \& Conquer, Time-Efficient, Subspace Graphs, Quantum Walks, Switching Networks, Directed st-Connectivity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.31
Quantum Advantage and Lower Bounds in Parallel Query Complexity

Authors: Joseph Carolan, Amin Shiraz Gilani, and Mahathi Vempati

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
It is well known that quantum, randomized and deterministic (sequential) query complexities are polynomially related for total boolean functions. We find that significantly larger separations between the parallel generalizations of these measures are possible. In particular, 1) We employ the cheatsheet framework to obtain an unbounded parallel quantum query advantage over its randomized analogue for a total function, falsifying a conjecture of [https://arxiv.org/abs/1309.6116]. 2) We strengthen 1 by constructing a total function which exhibits an unbounded parallel quantum query advantage despite having no sequential advantage, suggesting that genuine quantum advantage could occur entirely due to parallelism. 3) We construct a total function that exhibits a polynomial separation between 2-round quantum and randomized query complexities, contrasting a result of [https://arxiv.org/abs/1001.0018] that there is at most a constant separation for 1-round (nonadaptive) algorithms. 4) We develop a new technique for deriving parallel quantum lower bounds from sequential upper bounds. We employ this technique to give lower bounds for Boolean symmetric functions and read-once formulas, ruling out large parallel query advantages for them. We also provide separations between randomized and deterministic parallel query complexities analogous to items 1-3.
Cite as

Joseph Carolan, Amin Shiraz Gilani, and Mahathi Vempati. Quantum Advantage and Lower Bounds in Parallel Query Complexity. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{carolan_et_al:LIPIcs.ITCS.2025.31,
  author =	{Carolan, Joseph and Gilani, Amin Shiraz and Vempati, Mahathi},
  title =	{{Quantum Advantage and Lower Bounds in Parallel Query Complexity}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.31},
  URN =		{urn:nbn:de:0030-drops-226597},
  doi =		{10.4230/LIPIcs.ITCS.2025.31},
  annote =	{Keywords: Computational complexity theory, quantum, lower bounds, parallel}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.96
Formulations and Constructions of Remote State Preparation with Verifiability, with Applications

Authors: Jiayu Zhang

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
Remote state preparation with verifiability (RSPV) is an important quantum cryptographic primitive [Alexandru Gheorghiu and Thomas Vidick, 2019; Jiayu Zhang, 2022]. In this primitive, a client would like to prepare a quantum state (sampled or chosen from a state family) on the server side, such that ideally the client knows its full description, while the server holds and only holds the state itself. In this work we make several contributions on its formulations, constructions and applications. In more detail: - We first work on the definitions and abstract properties of the RSPV problem. We select and compare different variants of definitions [Bennett et al., 2001; Alexandru Gheorghiu and Thomas Vidick, 2019; Jiayu Zhang, 2022; Alexandru Gheorghiu et al., 2022], and study their basic properties (like composability and amplification). - We also study a closely related question of how to certify the server’s operations (instead of solely the states). We introduce a new notion named remote operator application with verifiability (ROAV). We compare this notion with related existing definitions [Summers and Werner, 1987; Dominic Mayers and Andrew Chi-Chih Yao, 2004; Zhengfeng Ji et al., 2021; Tony Metger and Thomas Vidick, 2021; Anand Natarajan and Tina Zhang, 2023], study its abstract properties and leave its concrete constructions for further works. - Building on the abstract properties and existing results [Zvika Brakerski et al., 2023], we construct a series of new RSPV protocols. Our constructions not only simplify existing results [Alexandru Gheorghiu and Thomas Vidick, 2019] but also cover new state families, for example, states in the form of 1/√2 (|0⟩ + |x_0⟩ + |1⟩ |x_1⟩). All these constructions rely only on the existence of weak NTCF [Zvika Brakerski et al., 2020; Navid Alamati et al., 2022], without additional requirements like the adaptive hardcore bit property [Zvika Brakerski et al., 2018; Navid Alamati et al., 2022]. - As a further application, we show that the classical verification of quantum computations (CVQC) problem [Dorit Aharonov et al., 2010; Urmila Mahadev, 2018] could be constructed from assumptions on group actions [Navid Alamati et al., 2020]. This is achieved by combining our results on RSPV with group-action-based instantiation of weak NTCF [Navid Alamati et al., 2022], and then with the quantum-gadget-assisted quantum verification protocol [Ferracin et al., 2018].
Cite as

Jiayu Zhang. Formulations and Constructions of Remote State Preparation with Verifiability, with Applications. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 96:1-96:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zhang:LIPIcs.ITCS.2025.96,
  author =	{Zhang, Jiayu},
  title =	{{Formulations and Constructions of Remote State Preparation with Verifiability, with Applications}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{96:1--96:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.96},
  URN =		{urn:nbn:de:0030-drops-227245},
  doi =		{10.4230/LIPIcs.ITCS.2025.96},
  annote =	{Keywords: Quantum Cryptography, Remote State Preparation, Self-testing, Verification of Quantum Computations}
}
Document
DOI: 10.4230/LIPIcs.TQC.2021.5
Fault-Tolerant Syndrome Extraction and Cat State Preparation with Fewer Qubits

Authors: Prithviraj Prabhu and Ben W. Reichardt

Published in: LIPIcs, Volume 197, 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)

Abstract
We reduce the extra qubits needed for two fault-tolerant quantum computing protocols: error correction, specifically syndrome bit measurement, and cat state preparation. For fault-tolerant syndrome extraction, we show an exponential reduction in qubit overhead over the previous best protocol. For a weight-w stabilizer, we demonstrate that stabilizer measurement tolerating one fault (distance-three) needs at most ⌈ log₂ w ⌉ + 1 ancillas. If qubits reset quickly, four ancillas suffice. We also study the preparation of cat states, simple yet versatile entangled states. We prove that the overhead needed for distance-three fault tolerance is only logarithmic in the cat state size. These results could be useful both for near-term experiments with a few qubits, and for the general study of the asymptotic resource requirements of syndrome measurement and state preparation. For 'a' measured flag bits, there are 2^a possible flag patterns that can identify faults. Hence our results come from solving a combinatorial problem: the construction of maximal-length paths in the a-dimensional hypercube, corresponding to maximal-weight stabilizers or maximal-weight cat states.
Cite as

Prithviraj Prabhu and Ben W. Reichardt. Fault-Tolerant Syndrome Extraction and Cat State Preparation with Fewer Qubits. In 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 197, pp. 5:1-5:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{prabhu_et_al:LIPIcs.TQC.2021.5,
  author =	{Prabhu, Prithviraj and Reichardt, Ben W.},
  title =	{{Fault-Tolerant Syndrome Extraction and Cat State Preparation with Fewer Qubits}},
  booktitle =	{16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)},
  pages =	{5:1--5:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-198-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{197},
  editor =	{Hsieh, Min-Hsiu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2021.5},
  URN =		{urn:nbn:de:0030-drops-140001},
  doi =		{10.4230/LIPIcs.TQC.2021.5},
  annote =	{Keywords: Quantum error correction, fault tolerance, quantum state preparation, combinatorics}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2017.48
Overlapping Qubits

Authors: Rui Chao, Ben W. Reichardt, Chris Sutherland, and Thomas Vidick

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Abstract
An ideal system of n qubits has 2^n dimensions. This exponential grants power, but also hinders characterizing the system's state and dynamics. We study a new problem: the qubits in a physical system might not be independent. They can "overlap," in the sense that an operation on one qubit slightly affects the others. We show that allowing for slight overlaps, n qubits can fit in just polynomially many dimensions. (Defined in a natural way, all pairwise overlaps can be <= epsilon in n^{O(1/epsilon^2)} dimensions.) Thus, even before considering issues like noise, a real system of n qubits might inherently lack any potential for exponential power. On the other hand, we also provide an efficient test to certify exponential dimensionality. Unfortunately, the test is sensitive to noise. It is important to devise more robust tests on the arrangements of qubits in quantum devices.
Cite as

Rui Chao, Ben W. Reichardt, Chris Sutherland, and Thomas Vidick. Overlapping Qubits. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 48:1-48:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chao_et_al:LIPIcs.ITCS.2017.48,
  author =	{Chao, Rui and Reichardt, Ben W. and Sutherland, Chris and Vidick, Thomas},
  title =	{{Overlapping Qubits}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{48:1--48:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.48},
  URN =		{urn:nbn:de:0030-drops-81826},
  doi =		{10.4230/LIPIcs.ITCS.2017.48},
  annote =	{Keywords: Quantum computing, Qubits, Dimension test}
}
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