Quantum Operations Research Articles

The Radiation Field, at the Origin of the Quantum Canonical Operators

We show that the electromagnetic radiation field, conventionally introduced as a perturbation in quantum mechanics, is actually at the basis of the operator formalism. We first analyze the linear resonant response of the (continuous) variables x(t), p(t) of a harmonic oscillator to the full radiation field, i.e. the zero-point field plus an applied field playing the role of the driving force, and then extend the analysis to the response of a charged particle bound by a non-linear force, typically an atomic electron. This leads to the establishment of a one-to-one correspondence between the response functions and the respective quantum operators, and to the identification of the quantum commutator with the Poisson bracket of the response functions with respect to the normalized variables of the driving field. To complete the quantum description, a similar procedure is used to obtain the field operators as the response functions to the same normalized variables. The results allow us to draw important conclusions about the physical content of the quantum formalism, in particular about the meaning of the quantum expectation values and the coarse-grained nature of the quantum-mechanical description.

Analysis of the relationship between ambient dose, ambient dose equivalent and effective dose in operational neutron spectra.

This study examines the relationship between ambient dose H*, ambient dose equivalent H*(10), and effective dose E for external neutron irradiation over 163 operational spectra from different workplaces. The results show that H* provides a reasonable estimate with a controlled margin, even if overestimated, to assess E compared with H*(10), which can lead to a significant overestimation or underestimation of E depending on the neutron spectra. The results highlight the limitations of H*(10) and the superiority of H* in estimating E according to the requirements of the operational quantities, especially in environments with high-energy neutrons.

Encapsulated Atomic Hydrogen in Octamethyl-POSS Cages: A Pulsed EPR Study.

Encapsulated atomic hydrogen in polyhedral oligomeric silsesquioxane (POSS) cages is a promising candidate for spin-based quantum technologies. Key parameters such as spin relaxation times and magnetic interactions with surrounding electron and nuclear spins can be typically probed with advanced electron paramagnetic resonance (EPR) methods. Here we present a detailed pulsed EPR study of the species H@Si8O12R8 with R=CH3, namely encapsulated atomic hydrogen in the octamethyl POSS derivative. The temperature dependence of the spin-lattice relaxation rate 1/ is analyzed in terms of a Raman process with a Debye temperature of K and a thermally activated process with (552 cm-1), whereas, the phase memory time shows the typical shortening behaviour at K observed for all methyl-containing derivatives. The hyperfine coupling of the cage Si nuclei is measured by hyperfine sublevel correlation (HYSCORE) spectroscopy and is found to fulfil the so-called "matching condition" at the low-field EPR transition. The potential of this paramagnetic molecule to perform one-qubit quantum operations is probed by room-temperature Rabi oscillations.

Quantum Tensor-Product Decomposition from Choi-State Tomography

The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt or tensor-product decomposition. While quantum technological implementations of the former are thoroughly studied, entangling properties on the operator level are harder to extract in the quantum computational framework because of the exponential nature of sample complexity. Here, we present an algorithm for unbalanced partitions into a small subsystem and a large one (the environment) to compute the tensor-product decomposition of a unitary the effect of which on the small subsystem is captured in classical memory, while the effect on the environment is accessible as a quantum resource. This quantum algorithm may be used to make predictions about operator nonlocality and effective open quantum dynamics on a subsystem, as well as for finding low-rank approximations and low-depth compilations of quantum circuit unitaries. We demonstrate the method and its applications on a time-evolution unitary of an isotropic Heisenberg model in two dimensions. Published by the American Physical Society 2024

Quantum Enhancement in Dark Matter Detection with Quantum Computation.

We propose a novel method to significantly enhance the signal rate in qubit-based dark matter detection experiments with the help of quantum interference. Various quantum sensors possess ideal properties for detecting wavelike dark matter, and qubits, commonly employed in quantum computers, are excellent candidates for dark matter detectors. We demonstrate that, by designing an appropriate quantum circuit to manipulate the qubits, the signal rate scales proportionally to n_{q}^{2}, with n_{q} being the number of sensor qubits, rather than linearly with n_{q}. Consequently, in the dark matter detection with a substantial number of sensor qubits, a significant increase in the signal rate can be expected. We provide a specific example of a quantum circuit that achieves this enhancement by coherently combining the phase evolution in each individual qubit due to its interaction with dark matter. We also demonstrate that the circuit is fault tolerant to dephasing noises, a critical quantum noise source in quantum computers. The enhancement mechanism proposed here is applicable to various modalities for quantum computers, provided that the quantum operations relevant to enhancing the dark matter signal can be applied to these devices.

Spin-Lattice Relaxation and Spin-Phonon Coupling of ns1 Metal Ions at the Surface.

To use transition metal ions for spin-based applications, it is essential to understand fundamental contributions to electron spin relaxation in different ligand environments. For example, to serve as building blocks for a device, transition metal ion-based molecular qubits must be organized on surfaces and preserve long electron spin relaxation times, up to room temperature. Here we propose monovalent group 12 ions (Zn+ and Cd+) as potential electronic metal qubits with an ns1 ground state. The relaxation properties of Zn+ and Cd+, stabilized at the interface of porous aluminosilicates, are investigated and benchmarked against vanadium (3d1) and copper (3d9) ions. The spin-phonon coupling has been evaluated through DFT modeling and found to be negligible for the ns1 states, explaining the long coherence time, up to 2 μs, at room temperature. These so far unexplored metal qubits may represent viable candidates for room temperature quantum operations and sensing.

Correction of microwave pulse reflection by digital filters in superconducting quantum circuits

Abstract Reducing the control error is vital for high-fidelity digital and analog quantum operations. In superconducting circuits, one disagreeable error arises from the reflection of microwave signals due to impedance mismatch in the control chain. Here, we demonstrate a reflection cancelation method when considering that there are two reflection nodes on the control line. We propose to generate the pre-distortion pulse by passing the envelopes of the microwave signal through digital filters, which enables real-time reflection correction when integrated into the field-programmable gate array (FPGA). We achieve a reduction of single-qubit gate infidelity from 0.67% to 0.11% after eliminating microwave reflection. Real-time correction of microwave reflection paves the way for precise control and manipulation of the qubit state and would ultimately enhance the performance of algorithms and simulations executed on quantum processors.

Interconversion between block coherence and multipartite entanglement in many-body systems

Coherence is intrinsically related to projective measurement. When the fixed projective measurement involves higher-rank projectors, the coherence resource is referred to as block coherence, which comes from the superposition of orthogonal subspaces. Here, we establish a set of quantitative relations for the interconversion between block coherence and multipartite entanglement under the framework of the block-incoherent operations. It is found that the converted multipartite entanglement is upper bounded by the initial block coherence of single-party system. Moreover, the generated multipartite entanglement can be transferred to its subsystems and restored to block coherence of the initial single-party system by means of local block-incoherent operations and classical communication. In addition, when only the coarse-grained quantum operations are accessible for the ancillary subsystems, we further demonstrate that a lossless resource interconversion is still realizable, and give a concrete example in three four-level systems. Our results provide a versatile approach to utilize different quantum resources in a cyclic fashion.

MODIFICATION OF A QUANTUM-INSPIRED GENETIC ALGORITHM FOR NUMERICAL OPTIMIZATION USING QUDIT UNDER CONDITIONS OF SIMULATING QUANTUM DECOHERENCE

The genetic algorithm for numerical optimization (GA) of the metaheuristic class is a method for finding optimal solutions based on the biological principles of natural selection and variability. GA is characterized by high operating speed, resistance to noise in the data, low probability of hitting the local extremum of the multimodal objective function, as well as the simultaneous application of probabilistic and deterministic rules for generating search space points. An alternative to the classical GA is the quantum-inspired genetic algorithm for numerical optimization (QIGA), which has advantages that are unattainable for GA by using the concepts and principles of quantum computing. The article proposes a new approach to the implementation of a quantum-inspired genetic numerical optimization algorithm for searching for the global maximum of the objective function, based on modeling the functioning of the GA by simulating the execution of quantum calculations based on qudit in the conditions of the existence of quantum decoherence in the era of noisy medium-scale quantum algorithms. For this purpose, to carry out quantum operations of rotating the states of multilevel quantum systems, the paper presents a density matrix based on Heisenberg-Weyl operators as an analogue of the Bloch sphere for qudits. The simulation of quantum decoherence is interpreted from the point of view of the influence of extraneous noise emanating from the environment on the qudit and is presented as the use of a normal random variable with zero mathematical expectation and unit variance in quantum gates. At the same time, the work presents detailed pseudocodes of the functioning of both the most modified quantum-inspired genetic algorithm for numerical optimization and its individual operations. Testing is carried out by conducting computational experiments with the implementation of a modified algorithm on two-dimensional and multidimensional functions of test optimization problems, as well as when solving an applied optimization problem of planning hybrid flow production in the manufacturing industry based on financial costs and solving the problem of increasing forecasting accuracy based on compact extreme learning machines. The experimental results demonstrate the superiority of the new algorithm over QIGA and classical optimization algorithms in the accuracy of the solution, the speed of convergence with the target value of the global maximum and the execution time of the algorithm.

Enhancing African market predictions: Integrating quantum computing with Echo State Networks

The integration of Quantum Computing into Echo State Networks (ESN) materializes in the form of the Quantum Echo State Network (QESN), a methodological innovation that reshapes predictive analytics within the domain of artificial intelligence. This investigation harnesses the novel QESN model alongside traditional ESNs, deploying them within the dynamic and burgeoning financial market of Africa. Our focus zeroes in on the Google Stock Price dataset, which provides a rich tapestry of regional financial activity. The QESN model distinguishes itself by a complex interconnection of qubits that conduct quantum operations, offering a marked amplification of computational capability. The empirical analysis reveals that the QESN model’s predictive prowess substantially exceeds that of its ESN counterpart, achieving an unprecedentedly low Mean Squared Error (MSE) of 0.00021 in forecasting market trends. This exceptional figure redefines the standards of financial prediction models in African markets and establishes the QESN as an instrumental breakthrough, providing unparalleled accuracy in the analysis and prediction of financial data.

Rényi mutual information in quantum field theory, tensor networks, and gravity

We explore a large class of correlation measures called the α − z Rényi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of Rényi entropies, the α − z RMIs are positive semi-definite and monotonically decreasing under local quantum operations, making them sensible measures of total (quantum and classical) correlations. This follows from their descendance from Rényi relative entropies. In addition to upper bounding connected correlation functions between subsystems, we prove the much stronger statement that for certain values of α and z, the α − z RMIs also lower bound certain connected correlation functions. We develop an easily implementable replica trick which enables us to compute the α − z RMIs in a variety of many-body systems including conformal field theories, free fermions, random tensor networks, and holography.

Relativistic Consistency of Nonlocal Quantum Correlations.

What guarantees the "peaceful coexistence" of quantum nonlocality and special relativity? The tension arises because entanglement leads to locally inexplicable correlations between distant events that have no absolute temporal order in relativistic spacetime. This paper identifies a relativistic consistency condition that is weaker than Bell locality but stronger than the no-signaling condition meant to exclude superluminal communication. While justifications for the no-signaling condition often rely on anthropocentric arguments, relativistic consistency is simply the requirement that joint outcome distributions for spacelike separated measurements (or measurement-like processes) must be independent of their temporal order. This is necessary to obtain consistent statistical predictions across different Lorentz frames. We first consider ideal quantum measurements, derive the relevant consistency condition on the level of probability distributions, and show that it implies no-signaling (but not vice versa). We then extend the results to general quantum operations and derive corresponding operator conditions. This will allow us to clarify the relationships between relativistic consistency, no-signaling, and local commutativity. We argue that relativistic consistency is the basic physical principle that ensures the compatibility of quantum statistics and relativistic spacetime structure, while no-signaling and local commutativity can be justified on this basis.

Optimal Zeno Dragging for Quantum Control: A Shortcut to Zeno with Action-Based Scheduling Optimization

The quantum Zeno effect asserts that quantum measurements inhibit simultaneous unitary dynamics when the “collapse” events are sufficiently strong and frequent. This applies in the limit of strong continuous measurement or dissipation. It is possible to implement a dissipative control that is known as “Zeno dragging” by dynamically varying the monitored observable, and hence also the eigenstates, which are attractors under Zeno dynamics. This is similar to adiabatic processes, in that the Zeno-dragging fidelity is highest when the rate of eigenstate change is slow compared to the measurement rate. We demonstrate here two theoretical methods for using such dynamics to achieve control of quantum systems. The first, which we shall refer to as “shortcut to Zeno,” is analogous to the shortcuts to adiabaticity (counterdiabatic driving) that are frequently used to accelerate unitary adiabatic evolution. In the second approach, we apply the Chantasri-Dressel-Jordan stochastic action [PRA 88, 042110 (2013)], and demonstrate that the extremal-probability readout paths derived from this are well suited to setting up a Pontryagin-style optimization of the Zeno-dragging schedule. A fundamental contribution of the latter approach is to show that an action suitable for measurement-driven control optimization can be derived quite generally from statistical arguments. Implementing these methods on the Zeno dragging of a qubit, we find that both approaches yield the same solution, namely, that the optimal control is a unitary that matches the motion of the Zeno-monitored eigenstate. We then show that such a solution can be more robust than a unitary-only operation and we comment on solvable generalizations of our qubit example embedded in larger systems. These methods open up new pathways toward systematically developing dynamic control of Zeno subspaces to realize dissipatively stabilized quantum operations. Published by the American Physical Society 2024

Computing Quantum Mean Values in the Deep Chaotic Regime.

We study the time evolution of mean values of quantum operators in a regime plagued by two difficulties: the smallness of ℏ and the presence of strong and ubiquitous classical chaos. While numerics become too computationally expensive for purely quantum calculations as ℏ→0, methods that take advantage of the smallness of ℏ-that is, semiclassical methods-suffer from both conceptual and practical difficulties in the deep chaotic regime. We implement an approach which addresses these conceptual problems, leading to a deeper understanding of the origin of the interference contributions to the operator's mean value. We show that in the deep chaotic regime our approach is capable of unprecedented accuracy, while a standard semiclassical method (the Herman-Kluk propagator) produces only numerical noise. Our work paves the way to the development and employment of more efficient and accurate methods for quantum simulations of systems with strongly chaotic classical limits.

Implications of the ICRU 95 quantities for various personal dosimetry techniques

The objective of this work is to assess the photon energy and angular response of various dosimetry systems in terms of the operational quantities for external radiation exposure personal dose, Hp, and personal absorbed dose in local skin, Dlocal skin, defined in Report 95 of the International Commission on Radiation Units and Measurements (ICRU). The dosimetry systems in Switzerland offer an opportunity to evaluate the status quo in personal dosimetry, due to variety of techniques employed and the possibility of accessing commissioning data from the various services.The photon energy and angular responses in terms of the ICRU Report 51 personal dose equivalents Hp(10) and Hp(0.07) were compiled for the dosimetry systems used by the Paul Scherrer Institute (radiophotoluminescence and direct ion storage), the Lausanne University Hospital (optically stimulated luminescence), the CERN (direct ion storage), Dosilab (thermoluminescence), and the SUVA (thermoluminescence). From this data, the response of the systems to the ICRU Report 95 quantities for whole body dosimetry (Hp) and skin dosimetry (Dlocal skin) was calculated using conversion coefficients from air kerma to the respective operational quantities. Regardless of the detector material, whole-body dosimeter design, or technique, each system over-estimated the personal dose, Hp, in the low-energy range (<70keV) up to a factor of 3 or 4. The indicated values for the personal absorbed dose in local skin, Dlocal skin, remains within the limits (0.71−1.67). These estimates highlight the impact of the ICRU 95 Report at a country’s scale and prompts discussion regarding potential solutions and challenges.

Estimation of H*(10) and E(Ω) (and H*) using the Hp(10) and Hp(0.07) detectors of a body TLD

The H*(10) and E(Ω) responses to photons from 15 to 1253 keV were determined as a function of source orientation for the 7LiF:Mg,Cu,P ‘body’ and ‘skin’ elements of a thermoluminescence dosemeter optimized to measure Hp(10) and Hp(0.07), and are presented here relative to the results from 662 keV calibration exposures. The calculations were performed using the Monte Carlo transport code MCNP6.2, with the dosemeter located either free-in-vacuo or on a concrete wall; the impacts of the radiation field and dosemeter mounting are discussed. The relative response profiles were found to be fairly flat at energies above a few 10s of keV, leading to the conclusion that the personal dosemeter may be used in some environmental or workplace fields to provide reasonable estimates of ambient dose equivalent and effective dose; the latter is additionally relevant given the newly proposed operational quantity ambient dose (H*). Optimal correction factors were also derived that allow the dosemeter's standard Hp(d,0°,137Cs) system calibrations to be maintained.

Symmetric Toeplitz Determinants for Classes Defined by Post Quantum Operators Subordinated to the Limaçon Function

The present extensive study is focused to find estimates for the upper bounds of the Toeplitz determinants. The logarithmic coefficients of univalent functions play an important role in different estimates in the theory of univalent functions, and in the this paper we derive the estimates of Toeplitz determinants and Toeplitz determinants of the logarithmic coefficients for the subclasses Ls𝑆𝑝𝑞 L𝑠C𝑝𝑞 and LsS𝑝𝑞 ∩ S, L𝑠𝐶𝑝𝑞 ∩ S, 0 q≤p≤10 𝑞≤𝑝≤1, defined by post quantum operators, which map the open unit disc 𝐷 onto the domain bounded by the limaçon curve defined by ∂Ds:={u+iv∈C:(u−1)2+v2−s4.2=4s2(u−1+s2)2+v2.}, where s∈−1,1.∖{0}. Keywords: Limaçon domain, subordination, (p, q)–derivative, Toeplitz and Hankel determinants, symmetric Toeplitz determinant, logarithmic coefficients, starlike functions with respect to symmetric points.

Present and new operational quantities evaluated from photon spectrum measurements at workplaces in the research reactor and accelerator facility at the JAEA

The International Commission on Radiation Units and Measurements (ICRU) has proposed to change the definitions of the operational quantities used for the area and individual monitoring of external exposure in ICRU Report 95. Since introducing new operational quantities into the radiation monitoring may affect the dose assessment using the present personal dosimeters, precise assessments of the influence on monitoring are necessary by characterizing the energy spectrum in the workplace and the energy dependency of the dosimeters to be used. This study measured photon spectra using a NaI(Tl) scintillation detector or a LaBr3(Ce) scintillation detector at the Japan Research Reactor No. 3 (JRR-3) and Japan Proton Accelerator Research Complex (J-PARC) workplaces at the Japan Atomic Energy Agency (JAEA). The photon energy spectra were obtained by unfolding the pulse height distributions measured at each workplace. The present and new operational quantities were then evaluated and compared using the spectra measured at the workplaces.In JRR-3, the photon energy spectra were measured at the workplaces in the reactor room and thermal neutron beam hall while the reactor was operated. The ambient dose equivalent rates H˙*(10) at the workplaces were 0.2 μSv·h−1 – 13 μSv·h−1. High energy gamma-rays of 6–7 MeV from 16N were observed near the fuel failure detection system in the reactor room. Those of 7–8 MeV produced by the thermal neutron capture of iron were observed in the reactor room and the beam hall. In J-PARC, the photon energy spectra were measured at the workplaces in the beam tunnel of the 3 GeV synchrotron beam ring five days after the operation. The ambient dose equivalent rates H˙*(10) at the workplaces were 35 μSv·h−1 –430 μSv·h−1.It was found that the new personal doses, Hp, were 10%–20% smaller than the present personal dose equivalents, Hp(10), at the workplaces.

Retrieving Nonlinear Features from Noisy Quantum States

Accurately estimating high-order moments of quantum states is an elementary precondition for many crucial tasks in quantum computing, such as entanglement spectroscopy, entropy estimation, spectrum estimation, and predicting nonlinear features from quantum states. But in reality, inevitable quantum noise prevents us from accessing the desired value. In this paper, we address this issue by systematically analyzing the feasibility and efficiency of extracting high-order moments from noisy states. We first show that there exists a quantum protocol capable of accomplishing this task if and only if the underlying noise channel is invertible. We then establish a method for deriving protocols that attain optimal sample complexity using quantum operations and classical postprocessing only. Our protocols, in contrast to conventional ones, incur lower overheads and avoid sampling different quantum operations due to a novel technique called the “‘observable shift method,” making the protocols strong candidates for practical use on current quantum devices. The proposed method also indicates the power of entangled protocols in retrieving high-order information, whereas in the existing methods, entanglement does not help. We further construct the protocol for large quantum systems to retrieve the depolarizing channels, making the proposed method scalable. Our work contributes to a deeper understanding of how quantum noise could affect high-order information extraction and provides guidance on how to tackle it. Published by the American Physical Society 2024

From Entanglement to Universality: A Multiparticle Spacetime Algebra Approach to Quantum Computational Gates Revisited

Alternative mathematical explorations in quantum computing can be of great scientific interest, especially if they come with penetrating physical insights. In this paper, we present a critical revisitation of our application of geometric (Clifford) algebras (GAs) in quantum computing as originally presented in [C. Cafaro and S. Mancini, Adv. Appl. Clifford Algebras 21, 493 (2011)]. Our focus is on testing the usefulness of geometric algebras (GAs) techniques in two quantum computing applications. First, making use of the geometric algebra of a relativistic configuration space (namely multiparticle spacetime algebra or MSTA), we offer an explicit algebraic characterization of one- and two-qubit quantum states together with a MSTA description of one- and two-qubit quantum computational gates. In this first application, we devote special attention to the concept of entanglement, focusing on entangled quantum states and two-qubit entangling quantum gates. Second, exploiting the previously mentioned MSTA characterization together with the GA depiction of the Lie algebras SO3;R and SU2;C depending on the rotor group Spin+3,0 formalism, we focus our attention to the concept of universality in quantum computing by reevaluating Boykin’s proof on the identification of a suitable set of universal quantum gates. At the end of our mathematical exploration, we arrive at two main conclusions. Firstly, the MSTA perspective leads to a powerful conceptual unification between quantum states and quantum operators. More specifically, the complex qubit space and the complex space of unitary operators acting on them merge in a single multivectorial real space. Secondly, the GA viewpoint on rotations based on the rotor group Spin+3,0 carries both conceptual and computational advantages compared to conventional vectorial and matricial methods.