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Heisenberg scaling based on population coding
IF 6.4 2区 物理与天体物理
Quantum Pub Date : 2025-02-26 DOI: 10.22331/q-2025-02-26-1648
Masahito Hayashi
{"title":"Heisenberg scaling based on population coding","authors":"Masahito Hayashi","doi":"10.22331/q-2025-02-26-1648","DOIUrl":"https://doi.org/10.22331/q-2025-02-26-1648","url":null,"abstract":"We study Heisenberg scaling of quantum metrology in the viewpoint of population coding. Although Fisher information has been used for a figure of merit to characterize Heisenberg scaling in quantum metrology, several studies pointed out it does not work as a figure of merit because it does not reflect the global structure. As an alternative figure of merit, we propose the mutual information, which connects the number of distinguishable elements of the parameter space in the viewpoint of population coding. We show that several unitary models achieve Heisenberg scaling in this context.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"10 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143495563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Simple and general bounds on quantum random access codes
IF 6.4 2区 物理与天体物理
Quantum Pub Date : 2025-02-25 DOI: 10.22331/q-2025-02-25-1643
Máté Farkas, Nikolai Miklin, Armin Tavakoli
{"title":"Simple and general bounds on quantum random access codes","authors":"Máté Farkas, Nikolai Miklin, Armin Tavakoli","doi":"10.22331/q-2025-02-25-1643","DOIUrl":"https://doi.org/10.22331/q-2025-02-25-1643","url":null,"abstract":"Random access codes are a type of communication task that is widely used in quantum information science. The optimal average success probability that can be achieved through classical strategies is known for any random access code. However, only a few cases are solved exactly for quantum random access codes. In this paper, we provide bounds for the fully general setting of n independent variables, each selected from a d-dimensional classical alphabet and encoded in a $D$-dimensional quantum system subject to an arbitrary quantum measurement. The bound recovers the exactly known special cases, and we demonstrate numerically that even though the bound is not tight overall, it can still yield a good approximation.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"27 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143495559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the locality of qubit encodings of local fermionic modes
IF 6.4 2区 物理与天体物理
Quantum Pub Date : 2025-02-25 DOI: 10.22331/q-2025-02-25-1644
Tommaso Guaita
{"title":"On the locality of qubit encodings of local fermionic modes","authors":"Tommaso Guaita","doi":"10.22331/q-2025-02-25-1644","DOIUrl":"https://doi.org/10.22331/q-2025-02-25-1644","url":null,"abstract":"Known mappings that encode fermionic modes into a bosonic qubit system are non-local transformations. In this paper we establish that this must necessarily be the case, if the locality graph is complex enough (for example for regular 2$d$ lattices). In particular we show that, in case of exact encodings, a fully local mapping is possible if and only if the locality graph is a tree. If instead we allow ourselves to also consider operators that only act fermionically on a subspace of the qubit Hilbert space, then we show that this subspace must be composed of long range entangled states, if the locality graph contains at least two overlapping cycles. This implies, for instance, that on 2$d$ lattices there exist states that are of low depth from the fermionic point of view, while in any encoding require a circuit of depth at least proportional to the system size to be prepared.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"85 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143495560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Virtual Quantum Device (VQD): A tool for detailed emulation of quantum computers
IF 6.4 2区 物理与天体物理
Quantum Pub Date : 2025-02-25 DOI: 10.22331/q-2025-02-25-1642
Cica Gustiani, Tyson Jones, Simon C. Benjamin
{"title":"The Virtual Quantum Device (VQD): A tool for detailed emulation of quantum computers","authors":"Cica Gustiani, Tyson Jones, Simon C. Benjamin","doi":"10.22331/q-2025-02-25-1642","DOIUrl":"https://doi.org/10.22331/q-2025-02-25-1642","url":null,"abstract":"We present the Virtual Quantum Device (VQD) platform, a system based on the QuEST quantum emulator. Through the use of VQDs, non-expert users can emulate specific quantum computers with detailed error models, bespoke gate sets and connectivities. The platform boasts an intuitive interface, powerful visualisation, and compatibility with high-performance computation for effective testing and optimisation of complex quantum algorithms or ideas across a range of quantum computing hardware. We create and explore five families of VQDs corresponding to trapped ions, nitrogen-vacancy-centres, neutral atom arrays, silicon quantum dot spins, and superconducting devices. Each is highly configurable through a set of tailored parameters. We showcase the key characteristics of each virtual device, providing practical examples of the tool's usefulness and highlighting each device's specific attributes. By offering user-friendly encapsulated descriptions of diverse quantum hardware, the VQD platform offers researchers the ability to rapidly explore algorithms and protocols in a realistic setting; meanwhile hardware experts can create their own VQDs to compare with their experiments.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"24 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143495558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Matrix-product unitaries: Beyond quantum cellular automata
IF 6.4 2区 物理与天体物理
Quantum Pub Date : 2025-02-25 DOI: 10.22331/q-2025-02-25-1645
Georgios Styliaris, Rahul Trivedi, David Perez-Garcia, J. Ignacio Cirac
{"title":"Matrix-product unitaries: Beyond quantum cellular automata","authors":"Georgios Styliaris, Rahul Trivedi, David Perez-Garcia, J. Ignacio Cirac","doi":"10.22331/q-2025-02-25-1645","DOIUrl":"https://doi.org/10.22331/q-2025-02-25-1645","url":null,"abstract":"Matrix-product unitaries (MPU) are 1D tensor networks describing time evolution and unitary symmetries of quantum systems, while their action on states by construction preserves the entanglement area law. MPU which are formed by a single repeated tensor are known to coincide with 1D quantum cellular automata (QCA), i.e., unitaries with an exact light cone. However, this correspondence breaks down for MPU with open boundary conditions, even if the resulting operator is translation-invariant. Such unitaries can turn short- to long-range correlations and thus alter the underlying phase of matter. Here we make the first steps towards a theory of MPU with uniform bulk but arbitrary boundary. In particular, we study the structure of a subclass with a direct-sum form which maximally violates the QCA property. We also consider the general case of MPU formed by site-dependent (nonuniform) tensors and show a correspondence between MPU and locally maximally entanglable states.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"68 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143495561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On multivariate polynomials achievable with quantum signal processing
IF 6.4 2区 物理与天体物理
Quantum Pub Date : 2025-02-20 DOI: 10.22331/q-2025-02-20-1641
Lorenzo Laneve, Stefan Wolf
{"title":"On multivariate polynomials achievable with quantum signal processing","authors":"Lorenzo Laneve, Stefan Wolf","doi":"10.22331/q-2025-02-20-1641","DOIUrl":"https://doi.org/10.22331/q-2025-02-20-1641","url":null,"abstract":"Quantum signal processing (QSP) is a framework which was proven to unify and simplify a large number of known quantum algorithms, as well as discovering new ones. QSP allows one to transform a signal embedded in a given unitary using polynomials. Characterizing which polynomials can be achieved with QSP protocols is an important part of the power of this technique, and while such a characterization is well-understood in the case of univariate signals, it is unclear which multivariate polynomials can be constructed when the signal is a vector, rather than a scalar. This work uses a slightly different formalism than what is found in the literature, and uses it to find simpler necessary conditions for decomposability, as well as a sufficient condition – the first, to the best of our knowledge, proven for a (generally inhomogeneous) multivariate polynomial in the context of quantum signal processing.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"14 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143451505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Potential and limitations of random Fourier features for dequantizing quantum machine learning
IF 6.4 2区 物理与天体物理
Quantum Pub Date : 2025-02-20 DOI: 10.22331/q-2025-02-20-1640
Ryan Sweke, Erik Recio-Armengol, Sofiene Jerbi, Elies Gil-Fuster, Bryce Fuller, Jens Eisert, Johannes Jakob Meyer
{"title":"Potential and limitations of random Fourier features for dequantizing quantum machine learning","authors":"Ryan Sweke, Erik Recio-Armengol, Sofiene Jerbi, Elies Gil-Fuster, Bryce Fuller, Jens Eisert, Johannes Jakob Meyer","doi":"10.22331/q-2025-02-20-1640","DOIUrl":"https://doi.org/10.22331/q-2025-02-20-1640","url":null,"abstract":"Quantum machine learning is arguably one of the most explored applications of near-term quantum devices. Much focus has been put on notions of variational quantum machine learning where $textit{parameterized quantum circuits}$ (PQCs) are used as learning models. These PQC models have a rich structure which suggests that they might be amenable to efficient dequantization via $textit{random Fourier features}$ (RFF). In this work, we establish necessary and sufficient conditions under which RFF does indeed provide an efficient dequantization of variational quantum machine learning for regression. We build on these insights to make concrete suggestions for PQC architecture design, and to identify structures which are necessary for a regression problem to admit a potential quantum advantage via PQC based optimization.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"25 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143451506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximating dynamical correlation functions with constant depth quantum circuits
IF 6.4 2区 物理与天体物理
Quantum Pub Date : 2025-02-19 DOI: 10.22331/q-2025-02-19-1639
Reinis Irmejs, Raul A. Santos
{"title":"Approximating dynamical correlation functions with constant depth quantum circuits","authors":"Reinis Irmejs, Raul A. Santos","doi":"10.22331/q-2025-02-19-1639","DOIUrl":"https://doi.org/10.22331/q-2025-02-19-1639","url":null,"abstract":"One of the most important quantities characterizing the microscopic properties of quantum systems are dynamical correlation functions. These correlations are obtained by time-evolving a perturbation of an eigenstate of the system, typically the ground state. In this work, we study approximations of these correlation functions that do not require time dynamics. We show that having access to a circuit that prepares an eigenstate of the Hamiltonian, it is possible to approximate the dynamical correlation functions up to exponential accuracy in the complex frequency domain $omega=Re(omega)+iIm(omega)$, on a strip above the real line $Im(omega)=0$. We achieve this by exploiting the continued fraction representation of the dynamical correlation functions as functions of frequency $omega$, where the level $k$ approximant can be obtained by measuring a weight $O(k)$ operator on the eigenstate of interest. In the complex $omega$ plane, we show how this approach allows to determine approximations to correlation functions with accuracy that increases exponentially with $k$.<br/> We analyse two algorithms to generate the continuous fraction representation in scalar or matrix form, starting from either one or many initial operators. We prove that these algorithms generate an exponentially accurate approximation of the dynamical correlation functions on a region sufficiently far away from the real frequency axis. We present numerical evidence of these theoretical results through simulations of small lattice systems. We comment on the stability of these algorithms with respect to sampling noise in the context of quantum simulation using quantum computers.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"41 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143443279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fermionic wave packet scattering: a quantum computing approach
IF 6.4 2区 物理与天体物理
Quantum Pub Date : 2025-02-19 DOI: 10.22331/q-2025-02-19-1638
Yahui Chai, Arianna Crippa, Karl Jansen, Stefan Kühn, Vincent R. Pascuzzi, Francesco Tacchino, Ivano Tavernelli
{"title":"Fermionic wave packet scattering: a quantum computing approach","authors":"Yahui Chai, Arianna Crippa, Karl Jansen, Stefan Kühn, Vincent R. Pascuzzi, Francesco Tacchino, Ivano Tavernelli","doi":"10.22331/q-2025-02-19-1638","DOIUrl":"https://doi.org/10.22331/q-2025-02-19-1638","url":null,"abstract":"Quantum computing provides a novel avenue towards simulating dynamical phenomena, and, in particular, scattering processes relevant for exploring the structure of matter. However, preparing and evolving particle wave packets on a quantum device is a nontrivial task. In this work, we propose a method to prepare Gaussian wave packets with momentum on top of the interacting ground state of a fermionic Hamiltonian. Using Givens rotation, we show how to efficiently obtain expectation values of observables throughout the evolution of the wave packets on digital quantum computers. We demonstrate our technique by applying it to the staggered lattice formulation of the Thirring model and studying the scattering of two wave packets. Monitoring the particle density and the entropy produced during the scattering process, we characterize the phenomenon and provide a first step towards studying more complicated collision processes on digital quantum computers. In addition, we perform a small-scale demonstration on IBM's quantum hardware, showing that our method is suitable for current and near-term quantum devices.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"13 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143443278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Information capacity of quantum communication under natural physical assumptions
IF 6.4 2区 物理与天体物理
Quantum Pub Date : 2025-02-18 DOI: 10.22331/q-2025-02-18-1637
Jef Pauwels, Stefano Pironio, Armin Tavakoli
{"title":"Information capacity of quantum communication under natural physical assumptions","authors":"Jef Pauwels, Stefano Pironio, Armin Tavakoli","doi":"10.22331/q-2025-02-18-1637","DOIUrl":"https://doi.org/10.22331/q-2025-02-18-1637","url":null,"abstract":"The quantum prepare-and-measure scenario has been studied under various physical assumptions on the emitted states. Here, we first discuss how different assumptions are conceptually and formally related. We then identify one that can serve as a relaxation of all others, corresponding to a limitation on the one-shot accessible information of the state ensemble. This motivates us to study the optimal state discrimination probability of a source subject to these various physical assumptions. We derive general and tight bounds for states restricted by their quantum dimension, their vacuum component, an arbitrary uniform overlap, the magnitude of higher-dimensional signals and the experimenter's trust in their device. Our results constitute a first step towards a more unified picture of semi-device-independent quantum information processing.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"23 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143443276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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