Quantum Resources Research Articles

A Dynamic Semi-Quantum Private Comparison Protocol for Size Relations

Abstract Semi-quantum private comparison allows multiple ``classical'' users who have restricted quantum capabilities to compare their private data with the assistance of a quantum third party. In this work, we propose a novel dynamic semi-quantum private comparison protocol using a circular transmission mode along with $d$-dimensional single-particle states. The protocol enables the comparison of data size relations among several ``classical'' users, while the third party can only determine the relative sizes without accessing the users' secret information. Security evaluations demonstrate that the designed protocol withstands typical external and internal attacks. Compared to previous works, this protocol offers several improvements: first, it supports dynamic addition or removal of users, enhancing applicability in practical scenarios; second, it eliminates the need for pre-shared keys, reducing quantum resource consumption; third, it avoids the use of high-dimensional multi-particle entangled states, thereby enhancing the feasibility of implementation. Therefore, the proposed protocol may have more practical potential compared to previous protocols.

The role of quantum resources in quantum energy teleportation

The role of quantum resources in quantum energy teleportation

Preparing remote states for genuine quantum networks

Quantum networks typically comprise quantum channels, repeaters, and end nodes. Remote state preparation (RSP) allows one end node to prepare the states of the other end nodes remotely. While quantum discord has recently been recognized as necessary for RSP, it does not guarantee the practical implementation of RSP in quantum networks surpasses any classical method. Herein, we theoretically introduce and experimentally study a quantum resource that we call the RSP capability. This resource validates all the static and dynamic elements required to enable genuine quantum networks where the RSP’s implementation can outperform any classical emulation of entanglement- and qubit-unitaries-free strategies, including the static resources of Einstein-Podolsky-Rosen pairs and the dynamic resources of quantum channels and repeaters. Our experiment measures the RSP capability to demonstrate the transition between classical and nonclassical RSP depending on the photon-pair qualities. It shows that quantum discord does not confirm a nonclassical RSP, but the RSP capability does. These results help reveal the quantum advantages that emerge when networking RSP is in play.

Dynamic quantum secret sharing with identity verification based on quantum walks

Abstract A dynamic quantum secret sharing protocol with authentication is proposed based on quantum walks. The protocol can share specific secrets and also update the secret information periodically based on the existing quantum walks structure. Participants can be added or removed while keeping the original secret unchanged. This is more flexible in practical applications. Before the secrets are shared, each participant is authenticated to ensure the legitimacy of all participants' identities. In addition, the protocol uses single photons as quantum resources, avoiding the complex preparation of entangled states, which makes the protocol more advantageous and potential in practical applications. Security analyses show that the protocol is resistant to collusion attack and other common attacks.

Qudit-based variational quantum eigensolver using photonic orbital angular momentum states.

Solving the electronic structure problem is a notorious challenge in quantum chemistry and material science. Variational quantum eigensolver (VQE) is a promising hybrid classical-quantum algorithm for finding the lowest-energy configuration of a molecular system. However, it typically requires many qubits and quantum gates with substantial quantum circuit depth to accurately represent the electronic wave function of complex structures. Here, we propose an alternative approach to solve the electronic structure problem using VQE with a single qudit. Our approach exploits a high-dimensional orbital angular momentum state of a heralded single photon and notably reduces the required quantum resources compared to conventional multi-qubit-based VQE. We experimentally demonstrate that our single-qudit-based VQE can efficiently estimate the ground state energy of hydrogen (H2) and lithium hydride (LiH) molecular systems corresponding to two- and four-qubit systems, respectively. We believe that our scheme opens a pathway to perform a large-scale quantum simulation for solving more complex problems in quantum chemistry and material science.

Random Natural Gradient

Hybrid quantum-classical algorithms appear to be the most promising approach for near-term quantum applications. An important bottleneck is the classical optimization loop, where the multiple local minima and the emergence of barren plateaux make these approaches less appealing. To improve the optimization the Quantum Natural Gradient (QNG) method \cite{stokes2020quantum} was introduced – a method that uses information about the local geometry of the quantum state-space. While the QNG-based optimization is promising, in each step it requires more quantum resources, since to compute the QNG one requires O(m2) quantum state preparations, where m is the number of parameters in the parameterized circuit. In this work we propose two methods that reduce the resources/state preparations required for QNG, while keeping the advantages and performance of the QNG-based optimization. Specifically, we first introduce the Random Natural Gradient (RNG) that uses random measurements and the classical Fisher information matrix (as opposed to the quantum Fisher information used in QNG). The essential quantum resources reduce to linear O(m) and thus offer a quadratic "speed-up", while in our numerical simulations it matches QNG in terms of accuracy. We give some theoretical arguments for RNG and then benchmark the method with the QNG on both classical and quantum problems. Secondly, inspired by stochastic-coordinate methods, we propose a novel approximation to the QNG which we call Stochastic-Coordinate Quantum Natural Gradient that optimizes only a small (randomly sampled) fraction of the total parameters at each iteration. This method also performs equally well in our benchmarks, while it uses fewer resources than the QNG.

Qubit-qubit quantum coherence mediated by an epsilon-near-zero waveguide

Quantum coherence, as a more general quantum resource compared to quantum entanglement, has attracted increasing attention over recent years. Establishing stable quantum coherence is crucial for implementing reliable quantum information tasks. In this study, we propose a scheme to generate stable quantum coherence of two qubits via an epsilon-near-zero (ENZ) waveguide. We find that employing Si3N4 rather than SiO2 results in stronger qubit-qubit coupling and maximal quantum coherence in a certain range. We derive analytical expressions for both quantum coherence and quantum entanglement, allowing for direct comparison within a unified framework. To achieve stable quantum coherence, classical field driving is introduced. We find that stable coherence is much larger and easier mediated than that of stable entanglement. Our work contributes to the creation of a new stable quantum resource via an ENZ waveguide.

Semi-quantum secret sharing protocol with specific bits based on third party

Abstract The fundamental concept of secret sharing involves dividing a secret into multiple parts and distributing them among several participants, who collectively safeguard the secret. When it comes to restoring the secret, cooperation among specific participants is necessary to reconstruct the original secret. Quantum secret sharing (QSS) employs quantum methods to address some limitations of classical secret sharing. Semi-QSS, an advancement of quantum methods, requires fewer quantum resources. Previous semi-quantum protocols demanded at least one participant with full quantum capabilities and randomly generated secret information. This paper introduces a protocol allowing three participants lacking complete quantum capabilities to share secret information of specific bits with the assistance of a third party possessing complete quantum capabilities. Unlike previous approaches, this protocol does not require participants to possess full quantum capabilities and shares secret information of specific bits. These characteristics make the protocol more practical and flexible for real-world applications.

Examining the quantum fisher information in the interaction of a dirac system with a squeezed generalized amplitude damping channel.

The inherent association between real quantum systems and their surrounding environment invariably results in decoherence, leading to the loss of entanglement. This diminution in entanglement coincides with a decline in the fidelity of transmitted information using the entangled quantum resource. This study scrutinizes the impact of the squeezed generalized amplitude damping (SGAD) channel on quantum Fisher information (QFI) parameters. The SGAD channel model, a versatile framework, is also employed to simulate other dissipative channels, including amplitude damping (AD) and generalized amplitude damping (GAD). Kraus operators facilitate the modeling of noisy channels. The results reveal that, within the SGAD channel, the QFI remains impervious to the squeezing variables (r and ). In the GAD channel, undergoes enhancement to a constant value with an upswing in temperature (T), while the parameter in the GAD channel, , akin to the SGAD channel, surges around T = 2 before complete loss ensues. Concerning the AD channel, the component of the QFI initially experiences decoherence with an augmentation in the AD noise parameter ( ). Subsequently, it is restored to its initial value with a further escalation in . Conversely, the component of the QFI in the AD channel experiences decoherence with an elevation in the AD noise parameter ( ).

Generation of squeezed vacuum state in the millihertz frequency band

The detection of gravitational waves has ushered in a new era of observing the universe. Quantum resource advantages offer significant enhancements to the sensitivity of gravitational wave observatories. While squeezed states for ground-based gravitational wave detection have received marked attention, the generation of squeezed states suitable for mid-to-low-frequency detection has remained unexplored. To address the gap in squeezed state optical fields at ultra-low frequencies, we report on the first direct observation of a squeezed vacuum field until Fourier frequency of 4 millihertz with the quantum noise reduction of up to 8.0 dB, by the employment of a multiple noise suppression scheme. Our work provides quantum resources for future gravitational wave observatories, facilitating the development of quantum precision measurement.

Approximate inference on optimized quantum Bayesian networks

In recent years, there has been a significant upsurge in the interest surrounding Quantum machine learning, with researchers actively developing methods to leverage the power of quantum technology for solving highly complex problems across various domains. However, implementing gate-based quantum algorithms on noisy intermediate quantum devices (NISQ) presents notable challenges due to limited quantum resources and inherent noise. In this paper, we propose an innovative approach for representing Bayesian networks on quantum circuits, specifically designed to address these challenges and highlight the potential of combining optimized circuits with quantum hybrid algorithms for Bayesian network inference. Our aim is to minimize the required quantum resource needed to implement a Quantum Bayesian network (QBN) and implement quantum approximate inference algorithm on a quantum computer. Through simulations and experiments on IBM Quantum computers, we show that our circuit representation significantly reduces the resource requirements without decreasing the performance of the model. These findings underscore how our approach can better enable practical applications of QBN on currently available quantum hardware.

Quantum circuit syntheses of Boolean matrix multiplication using only CNOT gates

Abstract Boolean matrices and operations on Boolean matrices have become increasingly popular in quantum computing and quantum information because they can be used to represent quantum states and the corresponding operations. In this paper, we first give a quantum circuit direct synthesis of general Boolean matrix multiplication using Toffoli gates. We assign a qubit to each element of the matrix and add Toffoli gates at the corresponding positions where the matrix elements are multiplied according to the arithmetic of matrix multiplication. For $n\times p$ dimensional matrix $A$ multiplied by $p\times m$ dimensional matrix $B$, $np + pm + nm$ qubits and at most $pmn$ Toffoli gates are used in total. Then, an improved heuristic algorithm based on matrix Hamming distance selection of CNOT gate is proposed to synthesize the quantum circuit of a matrix, without using wire switching and SWAP gates, using only CNOT gates. The results show that our method is as good as or better than the classical synthesis. Finally, the quantum circuit of Boolean matrix multiplication with at least one invertible or full-rank matrix using only CNOT gates is given, which is divided into five cases for discussion and analysis. For $n\times n$ dimensional invertible matrix $A$ multiplied by $n\times m$ dimensional matrix $B$, $nm$ qubits and at most $mn^{2}$ CNOT gates are used in total. For $n\times p$ dimensional column full-rank matrix $A$ multiplied by $p\times m$ dimensional matrix $B$, $nm$ qubits and at most $pmn$ CNOT gates are used in total. The results show that this method uses less quantum resources to synthesize the quantum circuit of Boolean matrix multiplication. The correctness of the quantum circuits was verified by the Aer simulator of the IBM Quantum platform.

Quantum anomaly detection in the latent space of proton collision events at the LHC

The ongoing quest to discover new phenomena at the LHC necessitates the continuous development of algorithms and technologies. Established approaches like machine learning, along with emerging technologies such as quantum computing show promise in the enhancement of experimental capabilities. In this work, we propose a strategy for anomaly detection tasks at the LHC based on unsupervised quantum machine learning, and demonstrate its effectiveness in identifying new phenomena. The designed quantum models-an unsupervised kernel machine and two clustering algorithms-are trained to detect new-physics events using a latent representation of LHC data, generated by an autoencoder designed to accommodate current quantum hardware limitations on problem size. For kernel-based anomaly detection, we implement an instance of the model on a quantum computer, and we identify a regime where it significantly outperforms its classical counterparts. We show that the observed performance enhancement is related to the quantum resources utilised by the model.

Toward a resource-optimized dynamic quantum algorithm via non-iterative auxiliary subspace corrections.

Recent quantum algorithms pertaining to electronic structure theory primarily focus on the threshold-based dynamic construction of ansatz by selectively including important many-body operators. These methods can be made systematically more accurate by tuning the threshold to include a greater number of operators into the ansatz. However, such improvements come at the cost of rapid proliferation of the circuit depth, especially for highly correlated molecular systems. In this work, we address this issue by the development of a novel theoretical framework that relies on the segregation of an ansatz into a dynamically selected core "principal" component, which is, by construction, adiabatically decoupled from the remaining operators. This enables us to perform computations involving the principal component using extremely shallow-depth circuits, whereas the effect of the remaining "auxiliary" component is folded into the energy function via a cost-efficient non-iterative correction, ensuring the requisite accuracy. We propose a formalism that analytically predicts the auxiliary parameters from the principal ones, followed by a suite of non-iterative auxiliary subspace correction techniques with different levels of sophistication. The auxiliary subspace corrections incur no additional quantum resources yet complement an inadequately expressive core of the ansatz to recover a significant amount of electronic correlations. We have numerically validated the resource efficiency and accuracy of our formalism with a number of strongly correlated molecular systems.

Magic of discrete Lattice Gauge theories

Simulation of quantum field theories and fundamental interactions is one of the most challenging tasks in modern particle physics. Classical computers generally fail to reproduce accurate results when it comes to strongly coupled theories such as QCD. Recent developments in quantum technologies open up the possibility of simulating such physical regimes by using quantum computers. In this paper, we study the quantum resource related to the simulability of a quantum theory, i.e. non-stabilizerness for Lattice Gauge Theory (LGT) with discrete symmetry gauge groups. We show that enforcing gauge constraints for [Formula: see text] LGTs has no cost in terms of this resource and discuss the relation between non-abelianity of the gauge group with the average non-stabilizerness of the gauge invariant Hilbert space.

Efficient multi-party quantum secret-sharing protocol

ContextQuantum secret sharing allows one secret dealer to divide his/her secret among different participants. Only when all the participants pool their secret pieces together can the secret be reconstructed. Quantum secret-sharing protocol can provide high security for users who need to share some secret information among some partners. It is also a useful tool in many applications such as secure operations of joint sharing of quantum money, sharing ancilla states, and distributed quantum computation. ObjectiveWe propose a novel multi-party quantum secret-sharing protocol (MPQSSP). MethodsIn our protocol, the dealer mixes the particle sequence of the Bell states and sends the sequence to the participants. The participants encode their secret pieces into Pauli operators, which are applied to the received particle sequence. After annularly transmitting and operating the particle sequence, the participants return the particle sequence to the dealer, who can share a secret with the partners by measuring the returned sequence with the Bell basis. ResultsThe proposed MPQSSP has the merits as follows. First, its qubit efficiency can be 100% when the sample bits of the secret and the corresponding sample qubits are ignored (In our protocol when the qubit efficiency is computed, the sample bits and the corresponding Bell states used to check eavesdropping are ignored). Second, it can protect participants' privacy and interests, since the dealer cannot derive the secret piece of any participant although he/she masters the secret. Third, the participants need not perform many quantum operations and measurements to check the eavesdropping, which helps improve the efficiency of the protocol. Fourth, compared with most of the similar MPQSSPs, the quantum resources of the proposed one are relatively easier to prepare. At last, the proposed protocol has the security against various eavesdropping attacks. ConclusionThe merits above show that Our MPQSSP is relatively more practical and efficient than similar ones.

Remote implementation of hidden or partially unknown quantum operators using optimal resources: a generalized view

Two protocols are proposed for two closely linked but different variants of remote implementation of quantum operators of specific forms The first protocol is designed for the remote implementation of the single qubit hidden quantum operator, whereas the second one is designed for the remote implementation of the partially unknown single qubit quantum operator. In both cases two-qubit maximally entangled state, which is entangled in the spatial degree of freedom is used. The quantum resources used here are optimal and easy to realize and maintain in comparison to the multi-partite or multi-mode entangled states used in earlier works. The impact of photon loss due to interaction with the environment is analyzed for both the schemes. The proposed protocols are also generalized to their controlled, bidirectional, cyclic, controlled cyclic, and controlled bidirectional versions and it is shown that either Bell state alone or products of Bell states will be sufficient to perform these tasks with some additional classical communications in the controlled cases only. This is in sharp contrast to the earlier proposals that require large entangled states. In addition, it’s noted that remote implementation of hidden or partially unknown operators involving multiple controllers and/or multiple players who jointly apply the desired operator(s) would require quantum channels more complex than the Bell states and their products. Explicit forms of such quantum channels are also provided.

Quantum enhanced multiple transmission estimation with a bright squeezed light field

Recently, there has been significant interest in multiple-parameter quantum estimation techniques that exploit quantum resources. In particular, the estimation of optical transmission is a crucial parameter in various scientific fields and industries. In optical-based sensing, precision can be enhanced through two approaches: increasing the number of photons that interact with the samples and utilizing quantum states of light. In this paper, we investigate multiple transmission estimation using bright two-mode squeezed states (bTMSSs), which combine the advantages of both bright light and quantum states. We calculate the precision bound for multiple transmission estimation by employing multiple copies of bTMSSs with experimentally feasible optimal measurement, determining both the quantum Cramer-Rao bound and the Cramer-Rao bound. Our results demonstrate that multiple copies of bTMSSs can achieve quantum-enhanced sensitivity for multiple transmissions compared to coherent states, and the ultimate limit of precision can be attained in regions with high nonlinear gain. Furthermore, as an application, we show the quantum-enhanced sensing in circular dichroism sensing using a pair of bTMSSs. Our strategy for multiple transmission estimation offers a practical platform for exploring real-world quantum sensing applications.

Scheme of preparing cluster states with cat qubits

Abstract Cluster states are essential quantum resources for one-way quantum computations and quantum networks. The reliable generation of cluster states in specific quantum systems is crucial for initializing complex quantum operations. In this paper, we introduce an efficient scheme for the deterministic preparation of a cluster state via circuit quantum electrodynamics (QED). Our scheme involves four individual microwave resonators, each of which is coupled to a superconducting transmon qutrit. We demonstrated that a four-cqubit cluster state can be achieved using three controlled-phase gate operations. The cluster state is prepared deterministically, eliminating the need for measurement-based feedback. Throughout these operations, the qutrit remains in its ground state, effectively minimizing decoherence from the qutrit. Numerical simulations suggest that our scheme can generate high-fidelity cluster states using current-circuit QED technology. We believe that our model will facilitate exploration of future large-scale continuous-variable quantum information processing systems.

Impossibility of universal work extraction from coherence: reconciling axiomatic and resource-theory approaches

Abstract We compare how the impossibility of a universal work extractor from coherence arises from different approaches to quantum thermodynamics: an explicit protocol accounting for all relevant quantum resources, and axiomatic, information-theoretic constraints imposed by constructor theory. We first explain how the impossibility of a universal work extractor from coherence is directly implied by a recently proposed constructor-theoretic theorem based on distinguishability, which is scale- and dynamics- independent. Then we give an explicit demonstration of this result within quantum theory, by proving the impossibility of generalising a proposed quantum protocol for deterministically extracting work from coherence. We demonstrate a new connection between the impossibility of universal work extractors and constructor-based irreversibility, which was recently shown using the quantum homogenizer. Finally we discuss additional avenues for applying the constructor-theoretic formulation of work extraction to quantum thermodynamics, including the irreversibility of quantum computation and thermodynamics of multiple conserved quantities.