Classical Bits Research Articles

Efficient MPS representations and quantum circuits from the Fourier modes of classical image data

Machine learning tasks are an exciting application for quantum computers, as it has been proven that they can learn certain problems more efficiently than classical ones. Applying quantum machine learning algorithms to classical data can have many important applications, as qubits allow for dealing with exponentially more data than classical bits. However, preparing the corresponding quantum states usually requires an exponential number of gates and therefore may ruin any potential quantum speedups. Here, we show that classical data with a sufficiently quickly decaying Fourier spectrum after being mapped to a quantum state can be well-approximated by states with a small Schmidt rank (i.e., matrix-product states) and we derive explicit error bounds. These approximated states can, in turn, be prepared on a quantum computer with a linear number of nearest-neighbor two-qubit gates. We confirm our results numerically on a set of 1024×1024-pixel images taken from the `Imagenette' and DIV2K datasets. Additionally, we consider different variational circuit ansätze and demonstrate numerically that one-dimensional sequential circuits achieve the same compression quality as more powerful ansätze.

Quantum Advantage: A Single Qubit's Experimental Edge in Classical Data Storage.

We implement an experiment on a photonic quantum processor establishing efficacy of the elementary quantum system in classical information storage. The advantage is established by considering a class of simple bipartite games played with the communication resource qubit and classical bit (c bit), respectively. Conventional wisdom, supported by the no-go theorems of Holevo and Frenkel-Weiner, suggests that such a quantum advantage is unattainable when the sender and receiver share randomness or classical correlations. However, our results reveal a quantum advantage in a scenario devoid of any shared randomness. Our experiment involves the development of a variational triangular polarimeter, enabling the realization of positive operator value measurements crucial for establishing the targeted quantum advantage. Beyond showcasing a robust communication advantage with a single qubit, our work paves the way for immediate applications in near-term quantum technologies. It provides a semi-device-independent certification scheme for quantum encoding-decoding systems and offers an efficient method for information loading and transmission in quantum networks.

Efficient Quantum Private Comparison with Unitary Operations

Quantum private comparison (QPC) is a crucial component of quantum multiparty computing (QMPC), allowing parties to compare their private inputs while ensuring that no sensitive information is disclosed. Many existing QPC protocols that utilize Bell states encounter efficiency challenges. In this paper, we present a novel and efficient QPC protocol that capitalizes on the distinct characteristics of Bell states to enable secure comparisons. Our method transforms private inputs into unitary operations on shared Bell states, which are then returned to a third party to obtain the comparison results. This approach enhances efficiency and decreases the reliance on complex quantum resources. A single Bell state can compare two classical bits, achieving a qubit efficiency of 100%. We illustrate the feasibility of the protocol through a simulation on the IBM Quantum Cloud Platform. The security analysis confirms that our protocol is resistant to both eavesdropping and attacks from participants.

Communication Complexity of Entanglement-Assisted Multi-Party Computation.

We consider a quantum and a classical version of a multi-party function computation problem with n players, where players 2,…,n need to communicate appropriate information to player 1 so that a "generalized" inner product function with an appropriate promise can be calculated. In the quantum version of the protocol, the players have access to entangled qudits but the communication is still classical. The communication complexity of a given protocol is the total number of classical bits that need to be communicated. When n is prime, and for our chosen function, we exhibit a quantum protocol (with complexity (n-1)(logn) bits) and a classical protocol (with complexity ((n-1)2(logn2) bits)). Furthermore, we present an integer linear programming formulation for determining a lower bound on the classical communication complexity. This demonstrates that our quantum protocol is strictly better than classical protocols.

The Effect of Linear Discriminant Analysis and Quantum Feature Maps on QSVM Performance for Obesity Diagnosis

Obesity, characterized by an excessive increase in body fat, is not only a significant disease but also a condition that serves as the basis for many other illnesses. Therefore, early intervention and necessary precautions for diagnosing and treating obesity are of paramount importance. Classical machine learning algorithms are actively utilized in medical fields to expedite prediction processes. However, the increasing volume of data renders even effective classification algorithms inadequate for experts to diagnose diseases. Quantum computing-based algorithms come into play at this point, offering a new perspective in machine learning by utilizing quantum physics, which is contrary to the rules of classical physics. Dimensionality reduction techniques required for the use of quantum-based algorithms play an essential role in both classical and quantum applications. In this study, Linear Discriminant Analysis (LDA) and Principal Component Analysis (PCA), classical dimensionality reduction methods, were applied to the obesity dataset and analyzed with Quantum Support Vector Machine (QSVM) and Support Vector Machine (SVM) algorithms. To conduct QSVM studies, the comparison of three different quantum feature maps providing the qubit transformation of classical bit data is also included in this study. As a result of the analysis, it was determined that the proposed method as LDA-QSVM achieved 100% success when used with Z and Pauli X feature maps. This success, which is rare in literature studies on obesity data, emphasizes the future potential of quantum-based algorithms in obesity diagnosis and treatment.

Quantum Software Encompasses Classical Software: Density Matrix from the Laplacian

It is widely understood that quantum computing — quantum gates upon qubits — is the general case, encompassing computing by classical means, viz. Boolean logic upon classical bits. It also seems reasonable that Quantum Software should encompass Classical Software. However, to accept such a statement regarding software, the feeling that it seems reasonable is not enough. One needs clear-cut definitions and formal conclusions. This is exactly the purpose of this paper. Previously, we have represented Classical Software by the Laplacian Matrix. More recently, we have shown that Quantum Software is faithfully represented by Density Matrices. It turns out that a Laplacian Matrix normalized by the Laplacian Trace easily obtains a Density Matrix. This opens the horizons for Quantum Software operations — such as unitary and reversible evolution — not naturally available with the classical Laplacian. This paper provides the necessary definitions and conclusions, illustrating the more general Quantum operations with a relevant case study, playing the double role of both classical and quantum software.

Assisted cloning of an unknown shared quantum state.

We first propose a novel protocol to realize quantum cloning of an arbitrary unknown shared state with assistance offered by a state preparer. The initial phase of this protocol involves the utilization of quantum teleportation (QT), enabling the transfer of quantum information from an arbitrary number of senders to another arbitrary number of receivers through a maximally entangled GHZ-type state serving as a network channel, without centralizing the information at any specific location. In the second stage of this protocol, the state preparer performs a special single-qubit projective measurement and multiple Z-basis measurements and then communicates a number of classical bits corresponding to measurement results, the perfect copy or orthogonal-complementing copy of an unknown shared state can be produced at senders hands. Then, using a non-maximally entangled GHZ-type state instead of the aforementioned quantum channel, we extend the proposed protocol from three perspectives: projective measurement, positive operator-value measurement (POVM), and a single generalized Bell-state measurement. Our schemes can relay quantum information over a network without requiring fully trusted central or intermediate nodes, and none of participants can fully access the information.

Hybrid quantum search with genetic algorithm optimization

Quantum genetic algorithms (QGA) integrate genetic programming and quantum computing to address search and optimization problems. The standard strategy of the hybrid QGA approach is to add quantum resources to classical genetic algorithms (GA), thus improving their efficacy (i.e., quantum optimization of a classical algorithm). However, the extent of such improvements is still unclear. Conversely, Reduced Quantum Genetic Algorithm (RQGA) is a fully quantum algorithm that reduces the GA search for the best fitness in a population of potential solutions to running Grover’s algorithm. Unfortunately, RQGA finds the best fitness value and its corresponding chromosome (i.e., the solution or one of the solutions of the problem) in exponential runtime, O(2n/2), where n is the number of qubits in the individuals’ quantum register. This article introduces a novel QGA optimization strategy, namely a classical optimization of a fully quantum algorithm, to address the RQGA complexity problem. Accordingly, we control the complexity of the RQGA algorithm by selecting a limited number of qubits in the individuals’ register and fixing the remaining ones as classical values of ‘0’ and ‘1’ with a genetic algorithm. We also improve the performance of RQGA by discarding unfit solutions and bounding the search only in the area of valid individuals. As a result, our Hybrid Quantum Algorithm with Genetic Optimization (HQAGO) solves search problems in O(2(n−k)/2) oracle queries, where k is the number of fixed classical bits in the individuals’ register.

A primer for quantum computing and its applications to healthcare and biomedical research.

To introduce quantum computing technologies as a tool for biomedical research and highlight future applications within healthcare, focusing on its capabilities, benefits, and limitations. Investigators seeking to explore quantum computing and create quantum-based applications for healthcare and biomedical research. Quantum computing requires specialized hardware, known as quantum processing units, that use quantum bits (qubits) instead of classical bits to perform computations. This article will cover (1) proposed applications where quantum computing offers advantages to classical computing in biomedicine; (2) an introduction to how quantum computers operate, tailored for biomedical researchers; (3) recent progress that has expanded access to quantum computing; and (4) challenges, opportunities, and proposed solutions to integrate quantum computing in biomedical applications.

Qubit reset with a shortcut-to-isothermal scheme.

Landauer's principle shows that the minimum energy cost to reset a classical bit in a bath with temperature T is k_{B}Tln2 in the infinite time. However, the task to reset the bit in finite time has posted a new challenge, especially for quantum bit (qubit) where both the operation time and controllability are limited. We design a shortcut-to-isothermal scheme to reset a qubit in finite time τ with limited controllability. The energy cost is minimized with the optimal control scheme with and without bound. This optimal control scheme can provide a reference to realize qubit reset with minimum energy cost for the limited time.

Verifiable Blind Quantum Computing with Trapped Ions and Single Photons.

We report the first hybrid matter-photon implementation of verifiable blind quantum computing. We use a trapped-ion quantum server and a client-side photonic detection system networked via a fiber-optic quantum link. The availability of memory qubits and deterministic entangling gates enables interactive protocols without postselection-key requirements for any scalable blind server, which previous realizations could not provide. We quantify the privacy at ≲0.03 leaked classical bits per qubit. This experiment demonstrates a path to fully verified quantum computing in the cloud.

High-Speed Quantum Radio-Frequency-Over-Light Communication.

Quantum dense coding (QDC) means to transmit two classical bits by only transferring one quantum bit, which has enabled high-capacity information transmission and strengthened system security. Continuous-variable QDC offers a promising solution to increase communication rates while achieving seamless integration with classical communication systems. Here, we propose and experimentally demonstrate a high-speed quantum radio-frequency-over-light (RFOL) communication scheme based on QDC with an entangled state, and achieve a practical rate of 20Mbps through digital modulation and RFOL communication. This scheme bridges the gap between quantum technology and real-world communication systems, which bring QDC closer to practical applications and offer prospects for further enhancement of metropolitan communication networks.

A novel quantum dialogue without information leakage based on single photons in both polarization and spatial-mode degrees of freedom

This paper puts forward a novel quantum dialogue (QD) protocol without information leakage based on single photons in both polarization and spatial-mode degrees of freedom. In this protocol, the receiver sends his private message to the sender in the way of quantum secure direct communication; and the receiver decodes out the private message of the sender with the help of auxiliary single photons in two degrees of freedom, double controlled-not (CNOT) operations and an auxiliary classical bit sequence sent from the sender. As a result, no information leakage takes place. Moreover, this protocol is proven to defeat the intercept-resend attack, the measure-resend attack, the entangle-measure attack and the Trojan horse attack from an outside eavesdropper. This protocol only employs single photons in two degrees of freedom as quantum resource and needs single-photon measurements. The qubit efficiency of this protocol is as high as 66.7%.

Four-party quantum secure direct communication based on hyperentangled bell states

Quantum Secure Direct Communication (QSDC) is a promising approach for secure information exchange. This paper proposes an efficient and secure four-party QSDC scheme utilizing hyperentangled Bell states in the polarization degree of freedom, the first longitudinal momentum degree of freedom and the second longitudinal momentum degree of freedom. The four participants can perform different unitary operations to independently encode their secret messages onto photons in three degrees of freedom, subsequently transmitting them directly through the quantum channel. In this proposed protocol, each degree of freedom of the photon can effectively carry two bits of information. Each round of transmission by a photon enables the four legitimate participants to obtain six classical bits of information. Notably, when compared to other photons based single-degree-of-freedom QSDC network protocols, the capacity of proposed QSDC protocol is tripled. Therefore, it significantly enhances the information transmission capability. Furthermore, comprehensive security analysis shows that our QSDC network protocol can withstand various attacks from external eavesdroppers.

Solvable Model of Quantum-Darwinism-Encoding Transitions.

We propose a solvable model of quantum Darwinism to encoding transitions-abrupt changes in how quantum information spreads in a many-body system under unitary dynamics. We consider a random Clifford circuit on an expanding tree, whose input qubit is entangled with a reference. The model has a quantum Darwinism phase, where one classical bit of information about the reference can be retrieved from an arbitrarily small fraction of the output qubits, and an encoding phase where such retrieval is impossible. The two phases are separated by a mixed phase and two continuous transitions. We compare the exact result to a two-replica calculation. The latter yields a similar "annealed" phase diagram, which applies also to a model with Haar random unitaries. We relate our approach to measurement-induced phase transitions (MIPTs), by solving a modified model where an environment eavesdrops on an encoding system. It has a sharp MIPT only with full access to the environment.

The quest for harnessing nuclear effects in graphene-based devices

The recent successes of superconducting qubits and the demonstration of quantum supremacy over classical bits herald a new era for information processing. Yet, the field is still in its infancy and there exist viable alternative candidates that can also store quantum information. In this review, we will highlight ideas, attempts, and the experimental progress to address nuclear spins in graphene, a readily available Dirac semimetal that consists of a single layer of carbon atoms. Carbon isotopes with a nuclear spin are rare in natural graphene. However, it is possible to enrich the spin-bearing 13C isotopes to produce large-scale graphene sheets, which constitute the testbed to store, transport, and retrieve spin information, or to engineer nanostructures. Here, the hyperfine interaction between the electron spins and the nuclear spins serves as an experimental control knob and mediator to address nuclear polarization and nuclear spin coherence times through electrical measurements. The exploitation of nuclear spins in graphene is thus an alluring perspective. We will discuss methods to synthesize 13C graphene and show experimental approaches and challenges to exploit the relatively weak hyperfine interaction in two-dimensional 13C graphene devices. The ultimate purpose, i.e., the exploitation of nuclear spins in graphene for information processing, is not within reach, but its potential for future applications merits a revisit of the current state-of-the-art.

Deep Cryogenic Temperature CMOS Circuit and System Design for Quantum Computing Applications

Quantum computing is a fascinating and rapidly evolving field of technology that promises to revolutionize many areas of science, engineering, and society. The fundamental unit of quantum computing is the quantum bit that can exist in two or more states concurrently, as opposed to a classical bit that can only be either 0 or 1. Any subatomic element, including atoms, electrons, and photons, can be used to implement qubits. The chosen sub-atomic elements should have quantum mechanical properties. Most commonly, photons have been used to implement qubits. Qubits can be manipulated and read by applying external fields or pulses, such as lasers, magnets, or microwaves. Quantum computers are currently suffering from various complications such as size, operating temperature, coherence problems, entanglement, etc. The realization of quantum computing, a novel paradigm that uses quantum mechanical phenomena to do computations that are not possible with classical computers, is made possible, most crucially, by the need for a quantum processor and a quantum SOC. As a result, Cryo-CMOS technology can make it possible to integrate a Quantum system on a chip. Cryo-CMOS devices are electronic circuits that operate at cryogenic temperatures, usually below 77 K (−196 °C).

High-dimensional single photon based quantum secure direct communication using time and phase mode degrees

Quantum secure direct communication (QSDC) can guarantee security using the characteristics of quantum mechanics even when a message is directly transmitted through a quantum channel without using a secret key. However, the transmission rate of the QSDC is limited by the dead time of a single photon detector (SPD) as well as channel loss over the distance. To overcome this limited transmission rate, we propose a high-dimensional single photon-based QSDC protocol that applies two optical degrees of freedom: time and phase state. First, an N-dimensional time and phase state generation method that considers the dead time is proposed to minimize the measurement loss of a transmitted message. Second, among the two types of quantum states, the phase state with relatively low measurement efficiency is used only for eavesdropping detection, and the time state is used for sending messages with differential delay time bin-based encoding techniques. Lastly, we propose an efficient method for measuring N-dimensional time and phase-based quantum states and recovering classical bit information. This study performs security analysis against various attacks, and verifies the transmission rate improvement effect through simulation. The result indicates that our proposal can guarantee higher security and transmission rates compared to the conventional DL04 QSDC.

An In-Depth Analysis of Steganography Techniques: From Classical Edge Detection to Adaptive Approaches

This paper delves into the realm of steganography, focusing on the evolution of techniques employed to conceal data within digital images. Beginning with an exploration of the motivations behind information security and the role of cryptography, the paper introduces adaptive steganography as a discreet means of incorporating private data into a cover medium. The discussion then shifts to the three key factors in image steganography - resilience, capacity, and imperceptibility - forming the foundation of effective data hiding. The spatial and frequency domain methods are compared, with specific emphasis on the classical Least Significant Bit insertion and more advanced adaptive steganography techniques. The paper further introduces edge-based steganography, highlighting the advantage of manipulating edge areas for increased imperceptibility. Moving beyond definitions and types, the paper provides a comprehensive analysis of notable research works in the field, elucidating their objectives, methodologies, results, strengths, and limitations. The conclusion reflects on the dynamic landscape of steganography, acknowledging both achievements and areas for improvement.

Entanglement dynamics in U(1) symmetric hybrid quantum automaton circuits

We study the entanglement dynamics of quantum automaton (QA) circuits in the presence of U(1) symmetry. We find that the second Rényi entropy grows diffusively with a logarithmic correction as tln⁡t, saturating the bound established by Huang \cite{Huang_2020}. Thanks to the special feature of QA circuits, we understand the entanglement dynamics in terms of a classical bit string model. Specifically, we argue that the diffusive dynamics stems from the rare slow modes containing extensively long domains of spin 0s or 1s. Additionally, we investigate the entanglement dynamics of monitored QA circuits by introducing a composite measurement that preserves both the U(1) symmetry and properties of QA circuits. We find that as the measurement rate increases, there is a transition from a volume-law phase where the second Rényi entropy persists the diffusive growth (up to a logarithmic correction) to a critical phase where it grows logarithmically in time. This interesting phenomenon distinguishes QA circuits from non-automaton circuits such as U(1)-symmetric Haar random circuits, where a volume-law to an area-law phase transition exists, and any non-zero rate of projective measurements in the volume-law phase leads to a ballistic growth of the Rényi entropy.