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Deterministic quantum search with adjustable parameters: implementations and applications

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arXiv 2022年

作者： Li, Guanzhong Li, Lvzhou Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-sen University Guangzhou510006 China

Grover’s algorithm provides a quadratic speedup over classical algorithms to search for marked elements in an unstructured database. The original algorithm is probabilistic, returning a marked element with bounded error. There are several schemes to achieve the deterministic version, by using the generalized Grover’s iteration G(α, β):= Sr(β) So(α) composed of phase oracle So(α) and phase rotation Sr(β). However, in all the existing schemes the value range of α and β is limited;for instance, in the three early schemes α and β are determined by the proportion of marked states M/N. In this paper, we break through this limitation by presenting a search framework with adjustable parameters, which allows α or β to be arbitrarily given. The significance of the framework lies not only in the expansion of mathematical form, but also in its application value, as we present two disparate problems which we are able to solve deterministically using the proposed framework, whereas previous schemes are ineffective. © 2022, CC BY.

关键词： Iterative methods

Efficiently Verifiable quantum Advantage on Near-Term Analog quantum Simulators

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PRX quantum 2025年第1期6卷 010341-010341页

作者： Zhenning Liu Dhruv Devulapalli Dominik Hangleiter Yi-Kai Liu Alicia J. Kollár Alexey V. Gorshkov Andrew M. Childs Joint Center for Quantum Information and Computer Science NIST/University of Maryland College Park Maryland 20742 USA Joint Quantum Institute NIST/University of Maryland College Park Maryland 20742 USA Department of Computer Science University of Maryland College Park Maryland 20742 USA Simons Institute for the Theory of Computing University of California at Berkeley California 94720 USA Applied and Computational Mathematics Division National Institute of Standards and Technology (NIST) Gaithersburg Maryland 20899 USA Department of Physics University of Maryland College Park Maryland 20742 USA Institute for Advanced Computer Studies University of Maryland College Park Maryland 20742 USA

Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics. In this work, we propose a quantum advantage protocol based on single-step Feynman-Kitaev verification of an analog quantum simulation, in which the verifier need only run an O(λ2)-time classical computation, and the prover need only prepare O(1) samples of a history state and perform O(λ2) single-qubit measurements, for a security parameter λ. We also propose a near-term feasible strategy for honest provers and discuss potential experimental realizations.

关键词： quantum computers

Geometric structure and transversal logic of quantum Reed–Muller codes

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arXiv 2024年

作者： Barg, Alexander Coble, Nolan J. Hangleiter, Dominik Kang, Christopher Joint Center for Quantum Information and Computer Science University of Maryland & NIST United States Institute for Systems Research Department of Electrical & Computer Engineering University of Maryland United States Department of Computer Science University of Maryland College Park United States Simons Institute for the Theory of Computing University of California at Berkeley United States Department of Computer Science University of Chicago United States

Designing efficient and noise-tolerant quantum computation protocols generally begins with an understanding of quantum error-correcting codes and their native logical operations. The simplest class of native operations are transversal gates, which are naturally fault-tolerant. In this paper, we aim to characterize the transversal gates of quantum Reed–Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. We start our work by establishing a new geometric characterization of quantum RM codes via the Boolean hypercube and its associated subcube complex. More specifically, a set of stabilizer generators for a quantum RM code can be described via transversal X and Z operators acting on subcubes of particular dimensions. This characterization leads us to define subcube operators composed of single-qubit π/2k Z-rotations that act on subcubes of given dimensions. We first characterize the action of subcube operators on the code space: depending on the dimension of the subcube, these operators either (1) act as a logical identity on the code space, (2) implement non-trivial logic, or (3) rotate a state away from the code space. Second, and more remarkably, we uncover that the logic implemented by these operators corresponds to circuits of multi-controlled-Z gates that have an explicit and simple combinatorial description. Overall, this suite of results yields a comprehensive understanding of a class of natural transversal operators for quantum RM codes. Copyright © 2024, The Authors. All rights reserved.

关键词： quantum computers

quantum Hermitian conjugate and encoding unnormalized matrices

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arXiv 2025年

作者： Zenchuk, Alexander I. Qi, Wentao Wu, Junde Federal Research Center of Problems of Chemical Physics and Medicinal Chemistry RAS Moscow reg. Chernogolovka142432 Russia Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-sen University Guangzhou510006 China School of Mathematical Sciences Zhejiang University Hangzhou310027 China

We further develop the family of matrix-manipulation algorithms based on the encoding the matrix elements into the probability amplitudes of the pure superposition state of a certain quantum system. We introduce two extensions to these algorithms which allow (i) to perform Hermitian conjugation of matrices under consideration and (ii) to weaken the restriction to the absolute values of matrix elements unavoidably imposed by the normalization condition for a pure quantum state. Both these extensions are applied to the matrix multiplication algorithm. Controlled measurement of ancilla state is implemented to avoid the problem of small success probability in the measurement process. © 2025, CC BY.

关键词： Encoding (symbols)

Remarks on controlled measurement and quantum algorithm for calculating Hermitian conjugate

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arXiv 2025年

作者： Fel’dman, Edward B. Zenchuk, Alexander I. Qi, Wentao Wu, Junde Federal Research Center of Problems of Chemical Physics and Medicinal Chemistry RAS Moscow reg. Chernogolovka142432 Russia Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-sen University Guangzhou510006 China School of Mathematical Sciences Zhejiang University Hangzhou310027 China

We present two new aspects for the recently proposed algorithms for matrix manipulating based on the special encoding the matrix elements into the superposition state of a quantum system. First aspect is the controlled measurement which allows to avoid the problem of small access probability to the required ancilla state at the final step of algorithms needed to remove the garbage of the states. Application of controlled measurement to the earlier developed algorithm is demonstrated. The second aspect is the algorithm for calculating the Hermitian conjugate of an arbitrary matrix, which supplements the algorithms proposed earlier. The appropriate circuits are presented. © 2025, CC BY.

关键词： quantum electronics

Matrix encoding method in variational quantum singular value decomposition

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arXiv 2025年

We propose the variational quantum singular value decomposition based on encoding the elements of the considered matrix into the state of a quantum system of appropriate dimension. This method doesn’t use the expansion of this matrix in terms of the unitary matrices. Conditional measurement is involved to avoid small success probability in ancilla measurement. The objective function for maximization algorithm can be obtained probabilistically via measurement of the state of a one-qubit subsystem. The circuit requires O(log N) qubits for realization of this algorithm whose depths is O(log N) as well. © 2025, CC BY.

关键词： Singular value decomposition

Scalable and fault-tolerant preparation of encoded k-uniform states

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arXiv 2025年

作者： Majidy, Shayan Hangleiter, Dominik Gullans, Michael J. Department of Physics Harvard University CambridgeMA02138 United States Simons Institute for the Theory of Computing University of California BerkeleyCA94720 United States Joint Center for Quantum Information and Computer Science University of Maryland NIST College ParkMD20742 United States

k-uniform states are valuable resources in quantum information, enabling tasks such as teleportation, error correction, and accelerated quantum simulations. The practical realization of k-uniform states, at scale, faces major obstacles: verifying k-uniformity is as difficult as measuring code distances, and devising fault-tolerant preparation protocols further adds to the complexity. To address these challenges, we present a scalable, fault-tolerant method for preparing encoded k-uniform states, and we illustrate our approach using surface and color codes. We first present a technique to determine k-uniformity of stabilizer states directly from their stabilizer tableau. We then identify a family of Clifford circuits that ensures both fault tolerance and scalability in preparing these states. Building on the encoded k-uniform states, we introduce a hybrid physical–logical strategy that retains some of the error-protection benefits of logical qubits while lowering the overhead for implementing arbitrary gates compared to fully logical algorithms. We show that this hybrid approach can outperform fully physical implementations for resource-state preparation, as demonstrated by explicit constructions of k-uniform states. Copyright © 2025, The Authors. All rights reserved.

关键词： Color codes

Blind calibration of a quantum computer

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arXiv 2025年

作者： Jeanette, Liam M. Wilkens, Jadwiga Roth, Ingo Than, Anton Green, Alaina M. Hangleiter, Dominik Linke, Norbert M. Joint Quantum Institute University of Maryland College ParkMD20742 United States Duke Quantum Center Duke University DurhamNC27701 United States Institute for Integrated Circuits Johannes Kepler University Linz Linz4040 Austria Quantum Research Center Technology Innovation Institute Abu Dhabi United Arab Emirates Simons Institute for the Theory of Computing University of California at Berkeley BerkeleyCA94720 United States Joint Center for Quantum Information and Computer Science NIST University of Maryland College ParkMD20742 United States

quantum system calibration is limited by the ability to characterize a quantum state under unknown device errors. We develop an accurate calibration protocol that is blind to the precise preparation of a specific quantum state. It extracts device errors from simple tomographic data only, and does not require bespoke experiments for a priori specified error mechanisms. Using a trapped-ion quantum computer, we experimentally demonstrate the accuracy of the method by recovering intentional miscalibrations. We then use blind calibration to estimate the native calibration parameters of the experimental system. The recovered calibrations are close to directly measured values and perform similarly in predicting state properties. © 2025, CC BY.

关键词： quantum computers

(Sub)Exponential quantum Speedup for Optimization

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arXiv 2025年

作者： Leng, Jiaqi Wu, Kewen Wu, Xiaodi Zheng, Yufan Simons Institute for the Theory of Computing University of California Berkeley United States Department of Mathematics University of California Berkeley United States Department of EECS University of California Berkeley United States Department of Computer Science University of Maryland College Park United States Joint Center for Quantum Information and Computer Science University of Maryland United States

We demonstrate provable (sub)exponential quantum speedups in both discrete and continuous optimization, achieved through simple and natural quantum optimization algorithms, namely the quantum adiabatic algorithm for discrete optimization and quantum Hamiltonian descent for continuous optimization. Our result builds on the Gilyén–Hastings–Vazirani (sub)exponential oracle separation for adiabatic quantum computing. With a sequence of perturbative reductions, we compile their construction into two standalone objective functions, whose oracles can be directly leveraged by the plain adiabatic evolution and Schrödinger operator evolution for discrete and continuous optimization, respectively. Copyright © 2025, The Authors. All rights reserved.

关键词： quantum channel