This is the fourth major release of the xSPDE toolbox, which solves stochastic partial and ordinary differential equations, with applications in biology, chemistry, engineering, medicine, physics and quantum technologies. It computes statistical averages, including time-step and sampling error estimation. xSPDE can provide higher order convergence, Fourier spectra and probability densities. The toolbox has graphical output and $χ^{2}$ statistics, as well as weighted, projected, or forward-backward equations. It can generate input-output quantum spectra. The equations can have independent periodic, Dirichlet, and Neumann or Robin boundary conditions in any dimension, for any vector component, and at either end of any interval. xSPDE has functions that can numerically solve both ordinary and partial differential stochastic equations of any type, obtaining correlations, probabilities and averages. The toolbox has a core treating stochastic differential equations, with averages, probability distributions and full error estimates. There are stochastic extensions treating applications to partial differential equations, projected equations, quantum stochastic equations, master equations and quantum phase-space simulations including Gaussian boson sampling experiments.
This paper introduces the FermiFab toolbox for many-particle quantum systems. It is mainly concerned with the representation of (symbolic) fermionic wavefunctions and the calculation of corresponding reduced density matrices (RDMs). The toolbox transparently handles the inherent antisymmetrization of wavefunctions and incorporates the creation/annihilation formalism. Thus, it aims at providing a solid base for a broad audience to use fermionic wavefunctions with the same ease as matrices in Matlab, say. Leveraging symbolic computation, the toolbox can greatly simply tedious pen-and-paper calcu…
This manual describes the basic objectives, functionalities and uses of the toolbox for Maple (Maplesoft^TM) called Quantavo. It is intended to facilitate calculations both symbolically and numerically related to Quantum Optics. In particular the evolution, measurement and entanglement properties of quantum states in the Fock basis can be simulated with it. It is provided to the community as a free open source module.
Simulating quantum states on a classical computer is hard, typically requiring prohibitive resources in terms of memory and computational power. Efficient simulation, however, can be achieved for certain classes of quantum states, in particular the so-called Gaussian quantum states of continuous variable systems. In this work we introduce QuGIT - a python numerical toolbox based on symplectic methods specialized in efficiently simulating multimode Gaussian states and operations. QuGIT is exact, requiring no truncation of Hilbert space, and provides a wide range of Gaussian operations on arbitr…
We present an open-source computer program written in Python language for quantum measurement and related issues. In our program, quantum states and operators, including quantum gates, can be developed into a quantum-object function represented by a matrix. Build into the program are several measurement schemes, including von Neumann measurement and weak measurement. Various numerical simulation methods are used to mimic the real experiment results. We first provide an overview of the program structure and then discuss the numerical simulation of quantum measurement. We illustrate the program'…
OCTBEC is a Matlab toolbox designed for optimal quantum control, within the framework of optimal control theory (OCT), of Bose-Einstein condensates (BEC). The systems we have in mind are ultracold atoms in confined geometries, where the dynamics takes place in one or two spatial dimensions, and the confinement potential can be controlled by some external parameters. Typical experimental realizations are atom chips, where the currents running through the wires produce magnetic fields that allow to trap and manipulate nearby atoms. The toolbox provides a variety of Matlab classes for simulations…
In this tutorial we review the basic building blocks of Quantum Information Processing with cold trapped atomic-ions. We mainly focus on methods to implement single-qubit rotations and two-qubit entangling gates, which form a universal set of quantum gates. Different ion qubit choices and their respective gate implementations are described.
Aluminum gallium arsenide-on-insulator (AlGaAsOI) exhibits large $χ^\left(2\right)$ and $χ^\left(3\right)$ optical nonlinearities, a wide tunable bandgap, low waveguide propagation loss, and a large thermo-optic coefficient, making it an exciting platform for integrated quantum photonics. With ultrabright sources of quantum light established in AlGaAsOI, the next step is to develop the critical building blocks for chip-scale quantum photonic circuits. Here we expand the quantum photonic toolbox for AlGaAsOI by demonstrating edge couplers, 3-dB splitters, tunable interferometers, and waveguide …
We study the coupling between collective variables of atomic spin and light polarization in an ensemble of cold 87Rb probed with polarized light. The effects of multiple hyperfine levels manifest themselves as a rank-2 tensor polarizability, whose irreducible components can be selected by means of probe detuning. The D1 and D2 lines of Rb are explored and we identify different detunings which lead to Hamiltonians with different symmetries for rotations. As possible applications of these Hamiltonians, we describe schemes for spin squeezing, quantum cloning, quantum memory, and measuring atom nu…
We introduce tqix.pis, a library of tqix, for quantum dynamics simulation of spin ensembles. The library emulates a dynamic process by a quantum circuit, including initializing a quantum state, executing quantum operators, and measuring the final state. It utilizes collective processes in spin ensembles to reduce the dimension from exponentially to quadratically with the number of particles, i.e., the quantum state spans in Dicke basis. It also facilitates the simulation time with multi-core processors and Graphics Processing Units. The library is thus applicable for the simulation of ensemble…
We present and discuss perspectives of current developments on advanced quantum optical circuits monolithically integrated in the lithium niobate platform. A set of basic components comprising photon pair sources based on parametric down conversion (PDC), passive routing elements and active electro-optically controllable switches and polarisation converters are building blocks of a toolbox which is the basis for a broad range of diverse quantum circuits. We review the state-of-the-art of these components and provide models that properly describe their performance in quantum circuits. As an exa…
École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Max Planck Institute for the Structure and Dynamics of Matter（马克斯·普朗克物质结构与动力学研究所）；University of Oxford（牛津大学）；Rutherford Appleton Laboratory（卢瑟福·阿普尔顿实验室）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；Universidad Nacional de Colombia（哥伦比亚国立大学）；University of Zurich（苏黎世大学）
We introduce version 3 of NetKet, the machine learning toolbox for many-body quantum physics. NetKet is built around neural-network quantum states and provides efficient algorithms for their evaluation and optimization. This new version is built on top of JAX, a differentiable programming and accelerated linear algebra framework for the Python programming language. The most significant new feature is the possibility to define arbitrary neural network ansätze in pure Python code using the concise notation of machine-learning frameworks, which allows for just-in-time compilation as well as the i…
We develop a general theoretical framework for measurement protocols employing statistical correlations of randomized measurements. We focus on locally randomized measurements implemented with local random unitaries in quantum lattice models. In particular, we discuss the theoretical details underlying the recent measurement of the second Rényi entropy of highly mixed quantum states consisting of up to $10$ qubits in a trapped-ion quantum simulator [Brydges et al., Science 364, 260 (2019)]. We generalize the protocol to access the overlap of quantum states, prepared sequentially in an experime…
We present a general protocol for stabilizer measurements and pumping in a system of N superconducting qubits. We assume always-on, equal dispersive couplings to a single mode of a high-Q microwave resonator in the ultra-strong dispersive limit where the dispersive shifts largely exceed the spectral linewidth. In this limit, we show how to map the two eigenvalues of an arbitrary weight M < N Pauli operator, onto two quasi-orthogonal coherent states of the cavity. Together with a fast cavity readout, this enables the efficient measurement of stabilizer operators.
We study a superconducting circuit that can act as a toolbox to generate various Bogoliubov-linear and nonlinear quantum operations on the microwave photon modes of superconducting resonators within one single circuit. The quantum operations are generated by exploring dispersive four-wave mixing (FWM) processes involving the resonator modes. Different FWM geometries can be realized by adjusting the circuit parameters and by applying appropriate microwave drivings. We illustrate this scheme using a circuit made of two superconducting qubits that couple with each other. Each qubit couples with o…
We describe a versatile toolbox for the quantum simulation of many-body lattice models, capable of exploring the combined effects of background Abelian and non-Abelian gauge fields, bond and site disorder, and strong on-site interactions. We show how to control the quantum dynamics of particles trapped in lattice potentials by the photon-assisted tunneling induced by periodic drivings. This scheme is general enough to be applied to either bosons or fermions with the additional advantage of being non-perturbative. It finds an ideal application in microfabricated ion trap arrays, where the quant…
Quantum communication employs the counter-intuitive features of quantum physics to perform tasks that are im- possible in the classical world. It is crucial for testing the foundations of quantum theory and promises to rev- olutionize our information and communication technolo- gies. However, for two or more parties to execute even the simplest quantum transmission, they must establish, and maintain, a shared reference frame. This introduces a considerable overhead in communication resources, par- ticularly if the parties are in motion or rotating relative to each other. We experimentally demo…
We study quantum Maxwell's demon in a discrete space-time setup. We consider a collection of particles hopping on a one-dimensional chain and a semipermeable barrier that allows the particles to hop in only one direction. Our main result is a formulation of a local unitary dynamics describing the action of this barrier. Such dynamics utilises an auxiliary system $\mathcal{A}$ and we study how properties of $\mathcal{A}$ influence the behaviour of particles. An immediate consequence of unitarity is the fact that particles cannot be trapped on one side of the barrier forever, unless $\mathcal{A}…
With an ever-expanding ecosystem of noisy and intermediate-scale quantum devices, exploring their possible applications is a rapidly growing field of quantum information science. In this work, we demonstrate that variational quantum algorithms feasible on such devices address a challenge central to the field of quantum metrology: The identification of near-optimal probes and measurement operators for noisy multi-parameter estimation problems. We first introduce a general framework which allows for sequential updates of variational parameters to improve probe states and measurements and is wide…
Increasingly sophisticated programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large quantum systems is the source of their power, but also makes them difficult to control precisely or characterize accurately using measured classical data. We review recently developed protocols for probing the properties of complex many-qubit systems using measurement schemes that are practical using today's quantum platforms. In all these protocols, a quantum sta…
We propose the implementation of fast resonant gates in circuit quantum electrodynamics for quantum information processing. We show how a suitable utilization of three-level superconducting qubits inside a resonator constitutes a key tool to perform diverse two-qubit resonant gates, improving the operation speed when compared to slower dispersive techniques. To illustrate the benefit of resonant two-qubit gates in circuit QED, we consider the implementation of a two-dimensional cluster state in an array of N x N superconducting qubits by using resonant controlled-phase (CPHASE) and one-qubit g…
We outline a toolbox comprised of passive optical elements, single photon detection and superpositions of coherent states (Schrodinger cat states). Such a toolbox is a powerful collection of primitives for quantum information processing tasks. We illustrate its use by outlining a proposal for universal quantum computation. We utilize this toolbox for quantum metrology applications, for instance weak force measurements and precise phase estimation. We show in both these cases that a sensitivity at the Heisenberg limit is achievable.
We describe the quantum dynamics of a magnetic rigid rotor in the mesoscopic scale where the Einstein-De Haas effect is predominant. In particular, we consider a single-domain magnetic nanoparticle with uniaxial anisotropy in a magnetic trap. Starting from the basic Hamiltonian of the system under the macrospin approximation, we derive a bosonized Hamiltonian describing the center-of-mass motion, the total angular momentum, and the macrospin degrees of freedom of the particle treated as a rigid body. This bosonized Hamiltonian can be approximated by a simple quadratic Hamiltonian that captures…
RIKEN Center for Quantum Computing, RIKEN（RIKEN量子计算中心）；Institut quantique, Université de Sherbrooke（舍布鲁克大学量子研究所）；Peter Grünberg Institute -Quantum Control (PGI-8), Forschungszentrum Jülich GmbH（于利希研究中心彼得·格林伯格研究所-量子控制）；Technical University of Munich（慕尼黑工业大学）；International Centre for Theory of Quantum Technologies (ICTQT), University of Gdansk（格但斯克大学量子技术理论国际中心）；Global Research and Development Center for Business by Quantum-AI Technology (G-QuAT), National Institute of Advanced Industrial Science and Technology (AIST)（产业技术综合研究所量子AI技术商务全球研发中心）；IBM Quantum, IBM Research Europe（IBM欧洲研究院IBM量子部门）；Plaksha University（普拉克斯哈大学）
There is growing interest to investigate states of matter with topological order, which support excitations in the form of anyons, and which underly topological quantum computing. Examples of such systems include lattice spin models in two dimensions. Here we show that relevant Hamiltonians can be systematically engineered with polar molecules stored in optical lattices, where the spin is represented by a single electron outside a closed shell of a heteronuclear molecule in its rotational ground state. Combining microwave excitation with the dipole-dipole interactions and spin-rotation couplin…
The recent experimental observation of spinor self-ordering of ultracold atoms in optical resonators has set the stage for the exploration of emergent magnetic orders in quantum-gas--cavity systems. Based on this platform, we introduce a generic scheme for the implementation of long-range quantum spin Hamiltonians composed of various types of couplings, including Heisenberg and Dzyaloshinskii-Moriya interactions. Our model is comprised of an effective two-component Bose-Einstein condensate, driven by two classical pump lasers and coupled to a single dynamic mode of a linear cavity in a double …
ARC 3.0 is a modular, object-oriented Python library combining data and algorithms to enable the calculation of a range of properties of alkali and divalent atoms. Building on the initial version of the ARC library [N. Šibalić et al, Comput. Phys. Commun. 220, 319 (2017)], which focused on Rydberg states of alkali atoms, this major upgrade introduces support for divalent atoms. It also adds new methods for working with atom-surface interactions, for modelling ultracold atoms in optical lattices and for calculating valence electron wave functions and dynamic polarisabilities. Such calculations …
We provide a toolbox for continuous variables quantum state engineering and characterization of biphoton states produced by spontaneous parametric down conversion in a transverse pump configuration. We show that the control of the pump beam's incidence spot and angle corresponds to phase space displacements of conjugate collective continuous variables of the biphoton. In particular, we illustrate with numerical simulations on a semiconductor device how this technique can be used to engineer and characterize arbitrary states of the frequency and time degrees of freedom.
Ground-state preparation for a given Hamiltonian is a common quantum-computing task of great importance and has relevant applications in quantum chemistry, computational material modeling, and combinatorial optimization. We consider an approach to simulate dissipative non-Hermitian Hamiltonian quantum dynamics using Hamiltonian simulation techniques to efficiently recover the ground state of a target Hamiltonian. The proposed method facilitates the energy transfer by repeatedly projecting ancilla qubits to the desired state, rendering the effective non-Hermitian Hamiltonian evolution on the sy…
DisCoPy (Distributional Compositional Python) is an open source toolbox for computing with string diagrams and functors. In particular, the diagram data structure allows to encode various kinds of quantum processes, with functors for classical simulation and optimisation, as well as compilation and evaluation on quantum hardware. This includes the ZX calculus and its many variants, the parameterised circuits used in quantum machine learning, but also linear optical quantum computing. We review the recent developments of the library in this direction, making DisCoPy a toolbox for the quantum co…
The parity gate emerged recently as a promising resource for performing universal quantum computation with fermions using only linear interactions. Here we analyse the parity gate (P-gate) from a theoretical point of view in the context of quantum networks. We present several schemes for entanglement generation with P-gates and show that native networks simplify considerably the resources required for producing multi-qubit entanglement, like n-GHZ states. Other applications include a Bell-state analyser and teleportation. We also show that cluster state fusion can be performed deterministicall…
The determination of the state fidelity and the detection of entanglement are fundamental problems in quantum information experiments. We investigate how these goals can be achieved with a minimal effort. We show that the fidelity of GHZ and W states can be determined with an effort increasing only linearly with the number of qubits. We also present simple and robust methods for other states, such as cluster states and states in decoherence-free subspaces.
Prepare-and-measure (P&M) quantum networks are the basic building blocks of quantum communication and cryptography. These networks crucially rely on non-orthogonal quantum encodings to distribute quantum correlations, thus enabling superior communication rates and information-theoretic security. Here, we present a computational toolbox that is able to efficiently characterise the set of input-output probability distributions for any discrete-variable P&M quantum network, assuming only the inner-product information of the quantum encodings. Our toolbox is thus highly versatile and can be used t…
This article reviews recent hybrid approaches to optical quantum information processing, in which both discrete and continuous degrees of freedom are exploited. There are well-known limitations to optical single-photon-based qubit and multi-photon-based qumode implementations of quantum communication and quantum computation, when the toolbox is restricted to the most practical set of linear operations and resources such as linear optics and Gaussian operations and states. The recent hybrid approaches aim at pushing the feasibility, the efficiencies, and the fidelities of the linear schemes to …
Several schemes have been proposed to extend Quantum Key Distribution protocols aiming at improving their security or at providing new physical substrates for qubit implementation. We present a toolbox to jointly create, manipulate and measure qubits stored in polarization and transverse-modes degrees of freedom of single photons. The toolbox includes local operations on single qubits, controlled operations between the two qubits and projective measurements over a wide variety of non-local bases in the four dimensional space of states. We describe how to implement the toolbox to perform an ext…
QuSoft；Institute for Logic, Language and Computation, University of Amsterdam（阿姆斯特丹大学逻辑、语言与计算研究所）；Department of Mathematical Sciences, University of Copenhagen（哥本哈根大学数学科学系）；Mathematical Institute, Leiden University（莱顿大学数学研究所）；Korteweg-de Vries Institute for Mathematics, University of Amsterdam（阿姆斯特丹大学科特韦格-德弗里斯数学研究所）
In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become significant. In particular, we discuss the mean-field approximation of the Dirac equation for many-electron systems, and its self-consistent numerical solution by using either radial mesh or Gaussian basis sets. The former technique is appropriate for spherical symmetric problems, such as atoms, while the latter approach is better suited to study non-spherical non-p…
Analytically Continuing the Randomized Measurement Toolbox
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Purdue University（普渡大学）；Institute for Advanced Study（高等研究院）；University of Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CNRS（法国国家科学研究中心）；Quobly；Paul Scherrer Institute（保罗谢尔研究所）；ETH Zürich（苏黎世联邦理工学院）
Fundamental forces of Nature are described by field theories, also known as gauge theories, based on a local gauge invariance. The simplest of them is quantum electrodynamics (QED), which is an example of an Abelian gauge theory. Such theories describe the dynamics of massless photons and their coupling to matter. However, in two spatial dimension (2D) they are known to exhibit gapped phases at low temperature. In the realm of quantum spin systems, it remains a subject of considerable debate if their low energy physics can be described by emergent gauge degrees of freedom. Here we present a cl…
