Resource For Quantum Computation Research Articles

Complexity growth and the Krylov-Wigner function

For any state in a D-dimensional Hilbert space with a choice of basis, one can define a discrete version of the Wigner function — a quasi-probability distribution which represents the state on a discrete phase space. The Wigner function can, in general, take on negative values, and the amount of negativity in the Wigner function has an operational meaning as a resource for quantum computation. In this note, we study the growth of Wigner negativity for a generic initial state under time evolution with chaotic Hamiltonians. We introduce the Krylov-Wigner function, i.e., the Wigner function defined with respect to the Krylov basis (with appropriate phases), and show that this choice of basis minimizes the early time growth of Wigner negativity in the large D limit. We take this as evidence that the Krylov basis (with appropriate phases) is ideally suited for a dual, semi-classical description of chaotic quantum dynamics at large D. We also numerically study the time evolution of the Krylov-Wigner function and its negativity in random matrix theory for an initial pure state. We observe that the negativity broadly shows three phases: it rises gradually for a time of OD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ O\\left(\\sqrt{D}\\right) $$\\end{document}, then hits a sharp ramp and finally saturates close to its upper bound of D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{D} $$\\end{document}.

Graph states of atomic ensembles engineered by photon-mediated entanglement

Graph states are a broad family of entangled quantum states, each defined by a graph composed of edges representing the correlations between subsystems. Such states constitute versatile resources for quantum computation and quantum-enhanced measurement. Their generation and engineering require a high level of control over entanglement. Here we report on the generation of continuous-variable graph states of atomic spin ensembles, which form the nodes of the graph. We program the entanglement structure encoded in the graph edges by combining global photon-mediated interactions in an optical cavity with local spin rotations. By tuning the entanglement between two subsystems, we either localize correlations within each subsystem or enable Einstein–Podolsky–Rosen steering—a strong form of entanglement that enables the extraction of precise information from one subsystem through measurements on the other. We further engineer a four-mode square graph state, highlighting the flexibility of our approach. Our method is scalable to larger and more complex graphs, laying groundwork for measurement-based quantum computation and advanced protocols in quantum metrology.

On geometrical aspects of the graph approach to contextuality.

The connection between contextuality and graph theory has paved the way for numerous advancements in the field. One notable development is the realization that sets of probability distributions in many contextuality scenarios can be effectively described using well-established convex setsfrom graph theory. This geometric approach allowsfor a beautiful characterization of these sets.Theapplication of geometry is not limited to thedescription of contextuality sets alone; it also plays a crucial role in defining contextuality quantifiers based on geometric distances. These quantifiers are particularly significant in the context of the resource theory of contextuality, which emerged following the recognition of contextuality as a valuable resource for quantum computation. In this paper, we provide a comprehensive review of the geometric aspects of contextuality. Additionally, we use this geometry to define several quantifiers, offering the advantage of applicability to other approaches to contextuality where previously defined quantifiers may not be suitable. This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'.

Quantum Teleportation and Entanglement of the 5-Qubit State Over a GHZ-Like Channel

Quantum information processing has a wide range of uses, including the solution of complex algorithms, cryptography, dense coding, quantum computation, and quantum teleportation. Quantum entanglement, a phenomenon that is crucial to many different applications of quantum computation, is an essential resource for quantum computation, and the need for quantum circuits that generate entangled states is one of the ongoing needs for constructing quantum computers. In this study, we present a general approach to the design of quantum circuits that produce entangled states. The approach can be applied to the design of various entanglement circuits with any number of qubits (n-qubit systems), and it makes use of a set of CNOT and Hadamard gates, where the number of CNOT gates should always be (n-1) and each gate connects the two adjacent qubits. In this paper, a three-entangled teleportation scheme of a GHZ-like state (named after its inventor Greenberger-Horne-Zeilinger) through three particles as a quantum channel is presented. The probability of successful teleportation depends on the degree of entanglement of GHZ-like states. A 5-qubit quantum teleportation over a GHZ-like channel has also been used. And single-qubit gates are defined, which are Pauli gates. These gates are represented by arrays I, X, Y, and Z. The results in this paper are good and promising theoretical results in the field of quantum entanglement and quantum teleportation using the Mathematica program.

Scalable Multipartite Entanglement Created by Spin Exchange in an Optical Lattice.

Ultracold atoms in optical lattices form a competitive candidate for quantum computation owing to the excellent coherence properties, the highly parallel operations over spins, and the ultralow entropy achieved in qubit arrays. For this, a massive number of parallel entangled atom pairs have been realized in superlattices. However, the more formidable challenge is to scale up and detect multipartite entanglement, the basic resource for quantum computation, due to the lack of manipulations over local atomic spins in retroreflected bichromatic superlattices. In this Letter, we realize the functional building blocks in quantum-gate-based architecture by developing a cross-angle spin-dependent optical superlattice for implementing layers of quantum gates over moderately separated atoms incorporated with a quantum gas microscope for single-atom manipulation and detection. Bell states with a fidelity of 95.6(5)% and a lifetime of 2.20±0.13 s are prepared in parallel, and then connected to multipartite entangled states of one-dimensional ten-atom chains and two-dimensional plaquettes of 2×4 atoms. The multipartite entanglement is further verified with full bipartite nonseparability criteria. This offers a new platform toward scalable quantum computation and simulation.

Correlations and projective measurements in maximally entangled multipartite states

Multipartite quantum states constitute the key resource for quantum computation. The understanding of their internal structure is thus of great importance in the field of quantum information. This paper aims at examining the structure of multipartite maximally entangled pure states, using tools with a simple and intuitive physical meaning, namely, projective measurements and correlations. We first show how, in such states, a very simple relation arises between post-measurement expectation values and pre-measurement correlations. We then infer the consequences of this relation on the structure of the recently introduced entanglement metric, allowing us to provide an upper bound for the persistency of entanglement. The dependence of these features on the chosen measurement axis is underlined, and two simple optimization procedures are proposed, to find those maximizing the correlations. Finally, we apply our procedures onto some prototypical examples.

Harnessing Quantumness of States using Discrete Wigner Functions under (non)‐Markovian Quantum Channels

AbstractThe negativity of the discrete Wigner functions (DWFs) is a measure of non‐classicality and is often used to quantify the degree of quantum coherence in a system. The study of Wigner negativity and its evolution under different quantum channels can provide insight into the stability and robustness of quantum states under their interaction with the environment, which is essential for developing practical quantum computing systems. The variation of DWF negativity of qubit, qutrit, and two‐qubit systems under the action of (non)‐Markovian random telegraph noise (RTN) and amplitude damping (AD) quantum channels is investigated. Different negative quantum states that can be used as a resource for quantum computation and quantum teleportation are constructed. The success of quantum computation and teleportation is estimated for these states under (non)‐Markovian evolutions.

Experimental Test of High-Dimensional Quantum Contextuality Based on Contextuality Concentration.

Contextuality is a distinctive feature of quantum theory and a fundamental resource for quantum computation. However, existing examples of contextuality in high-dimensional systems lack the necessary robustness required in experiments. Here, we address this problem by identifying a family of noncontextuality inequalities whose maximum quantum violation grows with the dimension of the system. At first glance, this contextuality is the single-system version of multipartite Bell nonlocality taken to an extreme form. What is interesting is that the single-system version achieves the same degree of contextuality but uses a Hilbert space of lower dimension. That is, contextuality "concentrates" as the degree of contextuality per dimension increases. We show the practicality of this result by presenting an experimental test of contextuality in a seven-dimensional system. By simulating sequences of quantum ideal measurements with destructive measurements and repreparation in an all-optical setup, we report a violation of 68.7 standard deviations of the simplest case of the noncontextuality inequalities identified. Our results advance the investigation of high-dimensional contextuality, its connection to the Clifford algebra, and its role in quantum computation.

Avoiding symmetry roadblocks and minimizing the measurement overhead of adaptive variational quantum eigensolvers

Quantum simulation of strongly correlated systems is potentially the most feasible useful application of near-term quantum computers. Minimizing quantum computational resources is crucial to achieving this goal. A promising class of algorithms for this purpose consists of variational quantum eigensolvers (VQEs). Among these, problem-tailored versions such as ADAPT-VQE that build variational ansätze step by step from a predefined operator pool perform particularly well in terms of circuit depths and variational parameter counts. However, this improved performance comes at the expense of an additional measurement overhead compared to standard VQEs. Here, we show that this overhead can be reduced to an amount that grows only linearly with the number n of qubits, instead of quartically as in the original ADAPT-VQE. We do this by proving that operator pools of size 2n−2 can represent any state in Hilbert space if chosen appropriately. We prove that this is the minimal size of such "complete" pools, discuss their algebraic properties, and present necessary and sufficient conditions for their completeness that allow us to find such pools efficiently. We further show that, if the simulated problem possesses symmetries, then complete pools can fail to yield convergent results, unless the pool is chosen to obey certain symmetry rules. We demonstrate the performance of such symmetry-adapted complete pools by using them in classical simulations of ADAPT-VQE for several strongly correlated molecules. Our findings are relevant for any VQE that uses an ansatz based on Pauli strings.

Resources for Bosonic Quantum Computational Advantage.

Quantum computers promise to dramatically outperform their classical counterparts. However, the nonclassical resources enabling such computational advantages are challenging to pinpoint, as it is not a single resource but the subtle interplay of many that can be held responsible for these potential advantages. In this Letter, we show that every bosonic quantum computation can be recast into a continuous-variable sampling computation where all computational resources are contained in the input state. Using this reduction, we derive a general classical algorithm for the strong simulation of bosonic computations, whose complexity scales with the non-Gaussian stellar rank of both the input state and the measurement setup. We further study the conditions for an efficient classical simulation of the associated continuous-variable sampling computations and identify an operational notion of non-Gaussian entanglement based on the lack of passive separability, thus clarifying the interplay of bosonic quantum computational resources such as squeezing, non-Gaussianity, and entanglement.

Random walk and non-Gaussianity of the 3D second-quantized Schrödinger–Newton nonlocal soliton

Nonlocal quantum fluids emerge as dark-matter models and tools for quantum simulations and technologies. However, strongly nonlinear regimes, like those involving multi-dimensional self-localized solitary waves, are marginally explored for what concerns quantum features. We study the dynamics of 3D+1 solitons in the second-quantized nonlocal nonlinear Schrödinger–Newton equation. We theoretically investigate the quantum diffusion of the soliton center of mass and other parameters, varying the interaction length. 3D+1 simulations of the Ito partial differential equations arising from the positive P-representation of the density matrix validate the theoretical analysis. The numerical results unveil the onset of non-Gaussian statistics of the soliton, which may signal quantum-gravitational effects and be a resource for quantum computing. The non-Gaussianity arises from the interplay between the soliton parameter quantum diffusion and the stable invariant propagation. The fluctuations and the non-Gaussianity are universal effects expected for any nonlocality and dimensionality.

Scalable Measures of Magic Resource for Quantum Computers

Nonstabilizerness or magic resource characterizes the amount of non-Clifford operations needed to prepare quantum states. It is a crucial resource for quantum computing and a necessary condition for quantum advantage. However, quantifying magic resource beyond a few qubits has been a major challenge. Here, we introduce efficient measures of magic resource for pure quantum states with a sampling cost that is independent of the number of qubits. Our method uses Bell measurements over two copies of a state, which we implement in experiment together with a cost-free error-mitigation scheme. We show the transition of classically simulable stabilizer states into intractable quantum states on the IonQ quantum computer. For applications, we efficiently distinguish stabilizer and nonstabilizer states with low measurement cost even in the presence of experimental noise. Further, we propose a variational quantum algorithm to maximize our measure via the shift rule. Our algorithm can be free of barren plateaus even for highly expressible variational circuits. Finally, we experimentally demonstrate a Bell-measurement protocol for the stabilizer Rényi entropy as well as the Wallach-Meyer entanglement measure. Our results pave the way to understanding the nonclassical power of quantum computers, quantum simulators, and quantum many-body systems.6 MoreReceived 27 April 2022Accepted 6 December 2022DOI:https://doi.org/10.1103/PRXQuantum.4.010301Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum algorithmsQuantum benchmarkingQuantum computationQuantum correlations in quantum informationQuantum information theoryQuantum Information

Simulating lattice quantum electrodynamics on a quantum computer

U(1) lattice gauge theories (LGTs) offer a way to simulate quantum electrodynamics, one of the three forces unified by the Standard Model of particles physics. Here we provide complete, quantum-gate-by-quantum-gate algorithms to simulate U(1) LGTs on a fault-tolerant quantum computer. We further perform rigorous error analysis in order to derive concrete estimates of the quantum computational resources required for an accurate simulation of U(1) LGTs using a second-order product formula. We show that U(1) LGTs in any spatial dimension can be simulated using non-Clifford T gates, where T is the simulation time, N is the number of lattice sites, Λ is the truncation parameter for the bosonic gauge fields, and ε is the simulation error. This work paves the way towards fault-tolerant quantum simulations of physical models closely related to the Standard Model of particle physics.

Quantum hardware calculations of periodic systems with partition-measurement symmetry verification: Simplified models of hydrogen chain and iron crystals

Running quantum algorithms on real hardware is essential for understanding their strengths and limitations, especially in the noisy intermediate scale quantum (NISQ) era. Herein we focus on the practical aspect of quantum computational calculations of solid-state crystalline materials based on theory developed in our group by using real quantum hardware with a novel noise mitigation technique referred to as partition-measurement symmetry verification, which performs post-selection of shot counts based on $Z_{2}$ and $U_{1}$ symmetry verification. We select two periodic systems with different level of complexity for these calculations. One of them is the distorted hydrogen chain as an example of very simple systems, and the other one is iron crystal in the BCC and FCC phases as it is considered to be inaccessible by using classical computational wavefunction methods. The ground state energies are evaluated based on the translational quantum subspace expansion (TransQSE) method for the hydrogen chain, and periodic boundary condition adapted VQE for our iron models. By applying these techniques for the simplest 2 qubit iron model systems, the correlation energies obtained by the hardware calculations agree with those of the state-vector simulations within $\sim$5 kJ/mol. Although the quantum computational resources used for those experiments are still limited, the techniques applied to obtain our simplified models will be applicable in essentially the same manner to more complicated cases as quantum hardware matures.

Exponential Clustering of Bipartite Quantum Entanglement at Arbitrary Temperatures

Macroscopic quantum effects play central roles in the appearance of inexplicable phenomena in low-temperature quantum many-body physics. Such macroscopic quantumness is often evaluated using long-range entanglement, i.e., entanglement in the macroscopic length scale. The long-range entanglement not only characterizes the novel quantum phases but also serves as a critical resource for quantum computation. Thus, the problem that arises is under which conditions can the long-range entanglement be stable even at room temperatures. Here, we show that bi-partite long-range entanglement is unstable at arbitrary temperatures and exponentially decays with distance. Our theorem provides a no-go theorem on the existence of the long-range entanglement. The obtained results are consistent with the existing observations that long-range entanglement at non-zero temperatures can exist in topologically ordered phases, where tripartite correlations are dominant. In the derivation of our result, we introduce a quantum correlation defined by the convex roof of the standard correlation function. We establish an exponential clustering theorem for generic quantum many-body systems for such a quantum correlation at arbitrary temperatures, which yields our main result by relating quantum correlation to quantum entanglement. As a simple application of our analytical techniques, we derived a general limit on the Wigner-Yanase-Dyson skew information and the quantum Fisher information, which will attract significant attention in the field of quantum metrology. Our work reveals novel general aspects of low-temperature quantum physics and sheds light on the characterization of long-range entanglement.

Unveiling Quantum Entanglement in Many-Body Systems from Partial Information

Quantum entanglement is commonly assumed to be a central resource for quantum computing and quantum simulation. Nonetheless, the capability to detect it in many-body systems is severely limited by the absence of sufficiently scalable and flexible certification tools. This issue is particularly critical in situations where the structure of entanglement is a priori unknown, and where one cannot rely on existing entanglement witnesses. Here, we implement a scheme in which the knowledge of the mean value of arbitrary observables can be used to probe multipartite entanglement in a scalable, certified, and systematic manner. Specifically, we rely on positive semidefinite conditions, independent of partial-transposition-based criteria, necessarily obeyed if the data can be reproduced by a separable state. The violation of any of these conditions yields a specific entanglement witness, tailored to the data of interest, revealing the salient features of the data which are impossible to reproduce without entanglement. We validate this approach by probing theoretical many-body states of several hundreds of qubits relevant to existing experiments: a single-particle quench in a one-dimensional XX chain; a many-body quench in a two-dimensional XX model with 1/r3 interactions; and thermal equilibrium states of Heisenberg and transverse-field Ising chains. In all cases, these investigations have led us to discover new entanglement witnesses, some of which could be characterized analytically, generalizing existing results in the literature. In summary, our paper introduces a flexible data-driven entanglement detection technique for uncharacterized quantum many-body states, of immediate relevance to experiments in a quantum advantage regime.Received 11 August 2021Revised 2 December 2021Accepted 22 February 2022DOI:https://doi.org/10.1103/PRXQuantum.3.010342Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEntanglement detectionQuantum entanglementPhysical SystemsQuantum spin modelsTechniquesData analysisSemiclassical methodsQuantum InformationAtomic, Molecular & OpticalStatistical Physics

Fully device-independent model on quantum networks

The Bell inequality can provide a useful witness for device-independent applications with quantum (or postquantum) eavesdroppers. This feature holds only for single entangled systems. Our goal is to explore a device-independent model for quantum networks. We first propose a Bell inequality to verify the genuinely multipartite nonlocality of connected quantum networks including cyclic networks and universal quantum computational resources for a measurement-based computation model. This is further used to construct a monogamy relation in a fully device-independent model with multisource quantum resources. It is finally applied for multiparty quantum key distribution, blind quantum computation, and quantum secret sharing. The present model can inspire various large-scale applications on quantum networks in a device-independent manner.

Generation of four-mode cluster states based on cascade four-wave mixing process

As a crucial quantum resource for quantum computing and quantum information processing, cluster state has attracted extensive attention due to its unique entanglement properties and rich structures. In this work, we theoretically propose a scheme for generating four-mode entangled states based on cascaded four-wave mixing (FWM) process. The internal entanglement characteristics are studied by using the positivity under partial transposition criterion and eigenmode decomposition. In addition, the output entangled states are reconstructed and optimized by adjusting the relative phase of balanced homodyne detection and postprocessing the signal noise, and finally three four-mode cluster states with different structures are generated. Such a method can effectively reduce the excess noise induced by finite squeezing. Our theoretical results provide a reliable way of generating scalable continuous variable cluster states based on FWM process in atomic ensemble.

Complexity of Fermionic Dissipative Interactions and Applications to Quantum Computing

Interactions between particles are usually a resource for quantum computing, making quantum many-body systems intractable by any known classical algorithm. In contrast, noise is typically considered as being inimical to quantum many-body correlations, ultimately leading the system to a classically tractable state. This work shows that noise represented by two-body processes, such as pair loss, plays the same role as many-body interactions and makes otherwise classically simulable systems universal for quantum computing. We analyze such processes in detail and establish a complexity transition between simulable and nonsimulable systems as a function of a tuning parameter. We determine important classes of simulable and nonsimulable two-body dissipation. Finally, we show how using resonant dissipation in cold atoms can enhance the performance of two-qubit gates.

Hierarchical system mapping for large-scale fault-tolerant quantum computing

With respect to large-scale quantum computing, it is important to know precisely and quickly how much quantum computational resources are necessary to study components and the whole system. If such quantum resources are provided, how much performance a quantum computer provides is also a critical issue. Unfortunately, it is practically infeasible to deal with such problems with conventional methods based on a non-structured description about quantum algorithm. To overcome the problems, we propose a fast method by using a hierarchically structured description about quantum algorithm which is much more compact than the conventional method. During the process, the dedicated computing regions and their interconnection are dynamically mapped onto a structured quantum computing system architecture. In our study, the proposed method works very faster such as 1 h than 1500 days for Shor algorithm to factorize a 512-bit integer. Meanwhile, since the combination of structured code and architecture provides a high degree of locality, it requires less SWAP chains, and hence, it does not increase the quantum computation depth more than expected.