35 research outputs found
Deploying hybrid quantum-secured infrastructure for applications: When quantum and post-quantum can work together
Most currently used cryptographic tools for protecting data are based on
certain computational assumptions, which makes them vulnerable with respect to
technological and algorithmic developments, such as quantum computing. One
existing option to counter this potential threat is quantum key distribution,
whose security is based on the laws of quantum physics. Quantum key
distribution is secure against unforeseen technological developments. A second
approach is post-quantum cryptography, which is a set of cryptographic
primitives that are believed to be secure even against attacks with both
classical and quantum computing technologies. From this perspective, this study
reviews recent progress in the deployment of the quantum-secured infrastructure
based on quantum key distribution, post-quantum cryptography, and their
combinations. Various directions in the further development of the full-stack
quantum-secured infrastructure are also indicated. Distributed applications,
such as blockchains and distributed ledgers, are also discussed.Comment: 11 pages, 0 figures, 1 table; Perspective pape
Realization of quantum algorithms with qudits
The paradigm behind digital quantum computing inherits the idea of using
binary information processing. The nature in fact gives much more rich
structures of physical objects that can be used for encoding information, which
is especially interesting in the quantum mechanical domain. In this Colloquium,
we review several ideas indicating how multilevel quantum systems, also known
as qudits, can be used for efficient realization of quantum algorithms, which
are represented via standard qubit circuits. We focus on techniques of
leveraging qudits for simplifying decomposition of multiqubit gates, and for
compressing quantum information by encoding multiple qubits in a single qudit.
As we discuss, these approaches can be efficiently combined. This allows
reducing in the number of entangling (two-body) operations and the number of
the used quantum information carriers compared to straightforward qubit
realizations. These theoretical schemes can be implemented with quantum
computing platforms of various nature, such as trapped ions, neutral atoms,
superconducting junctions, and quantum light. We conclude with summarizing a
set of open problems, whose resolving is an important further step towards
employing universal qudit-based processors for running qubit algorithms.Comment: 24 pages, 19 figure
Fourier expansion in variational quantum algorithms
The Fourier expansion of the loss function in variational quantum algorithms
(VQA) contains a wealth of information, yet is generally hard to access. We
focus on the class of variational circuits, where constant gates are Clifford
gates and parameterized gates are generated by Pauli operators, which covers
most practical cases while allowing much control thanks to the properties of
stabilizer circuits. We give a classical algorithm that, for an -qubit
circuit and a single Pauli observable, computes coefficients of all
trigonometric monomials up to a degree in time bounded by
. Using the general structure and implementation of the
algorithm we reveal several novel aspects of Fourier expansions in
Clifford+Pauli VQA such as (i) reformulating the problem of computing the
Fourier series as an instance of multivariate boolean quadratic system (ii)
showing that the approximation given by a truncated Fourier expansion can be
quantified by the norm and evaluated dynamically (iii) tendency of
Fourier series to be rather sparse and Fourier coefficients to cluster together
(iv) possibility to compute the full Fourier series for circuits of non-trivial
sizes, featuring tens to hundreds of qubits and parametric gates.Comment: 10+5 pages, code available at https://github.com/idnm/FourierVQA,
comments welcom
Universal quantum computing with qubits embedded in trapped-ion qudits
Recent developments in qudit-based quantum computing, in particular with
trapped ions, open interesting possibilities for scaling quantum processors
without increasing the number of physical information carriers. In this work,
we propose a method for compiling quantum circuits in the case, where qubits
are embedded into qudits of experimentally relevant dimensionalities,
, for the trapped-ion platform. In particular, we demonstrate how
single-qubit, two-qubit, and multiqubit gates can be realized using
single-qudit operations and the Molmer-Sorensen (MS) gate as a basic
two-particle operation. We expect that our findings are directly applicable to
trapped-ion-based qudit processors.Comment: 7+2 pages, 4+2 figures, 1 tabl
One generalization of the Dicke-type models
We discuss one family of possible generalizations of the Jaynes-Cummings and
the Tavis-Cummings models using the technique of algebraic Bethe ansatz related
to the Gaudin-type models. In particular, we present a family of (generically)
non-Hermitian Hamiltonians that generalize paradigmatic quantum-optical models.
Further directions of our research include studying physical properties of the
obtained generalized models.Comment: 4 pages, 0 figure
Integrable Floquet systems related to logarithmic conformal field theory
We study an integrable Floquet quantum system related to lattice statistical
systems in the universality class of dense polymers. These systems are
described by a particular non-unitary representation of the Temperley-Lieb
algebra. We find a simple Lie algebra structure for the elements of
Temperley-Lieb algebra which are invariant under shift by two lattice sites,
and show how the local Floquet conserved charges and the Floquet Hamiltonian
are expressed in terms of this algebra. The system has a phase transition
between local and non-local phases of the Floquet Hamiltonian. We provide a
strong indication that in the scaling limit this non-equilibrium system is
described by the logarithmic conformal field theory.Comment: 22 pages, 2 figure
Multiclass classification using quantum convolutional neural networks with hybrid quantum-classical learning
Multiclass classification is of great interest for various applications, for example, it is a common task in computer vision, where one needs to categorize an image into three or more classes. Here we propose a quantum machine learning approach based on quantum convolutional neural networks for solving the multiclass classification problem. The corresponding learning procedure is implemented via TensorFlowQuantum as a hybrid quantum-classical (variational) model, where quantum output results are fed to the softmax activation function with the subsequent minimization of the cross entropy loss via optimizing the parameters of the quantum circuit. Our conceptional improvements here include a new model for a quantum perceptron and an optimized structure of the quantum circuit. We use the proposed approach to solve a 4-class classification problem for the case of the MNIST dataset using eight qubits for data encoding and four ancilla qubits; previous results have been obtained for 3-class classification problems. Our results show that the accuracy of our solution is similar to classical convolutional neural networks with comparable numbers of trainable parameters. We expect that our findings will provide a new step toward the use of quantum neural networks for solving relevant problems in the NISQ era and beyond
Minimizing the negativity of quantum circuits in overcomplete quasiprobability representations
The problem of simulatability of quantum processes using classical resources
plays a cornerstone role for quantum computing. Quantum circuits can be
simulated classically, e.g., using Monte Carlo sampling techniques applied to
quasiprobability representations of circuits' basic elements, i.e., states,
gates, and measurements. The effectiveness of the simulation is determined by
the amount of the negativity in the representation of these basic elements.
Here we develop an approach for minimizing the total negativity of a given
quantum circuit with respect to quasiprobability representations, that are
overcomplete, i.e., are such that the dimensionality of corresponding
quasistochastic vectors and matrices is larger than the squared dimension of
quantum states. Our approach includes both optimization over equivalent
quasistochastic vectors and matrices, which appear due to the overcompleteness,
and optimization over overcomplete frames. We demonstrate the performance of
the developed approach on some illustrative cases, and show its significant
advantage compared to the standard overcomplete quasistochastic
representations. We also study the negativity minimization of noisy brick-wall
random circuits via a combination of increasing frame dimension and applying
gate merging technique. We demonstrate that the former approach appears to be
more efficient in the case of a strong decoherence.Comment: 15 pages, 8 figure