Qubit Representation Research Articles

Construction of Antisymmetric Variational Quantum States with Real Space Representation.

Electronic state calculations using quantum computers are mostly based on the second quantized formulation, which is suitable for qubit representation. Another way to describe electronic states on a quantum computer is based on the first quantized formulation, which is expected to achieve smaller scaling with respect to the number of basis functions than the second quantized formulation. Among basis functions, a real space basis is an attractive option for quantum dynamics simulations in the fault-tolerant quantum computation (FTQC) era. A major difficulty in the first quantized algorithm with a real space basis is state preparation for many-body electronic systems. This difficulty stems from the antisymmetry of electrons, and it is not straightforward to construct antisymmetric quantum states on a quantum circuit. In this study, we provide a design principle for constructing variational quantum circuits to prepare an antisymmetric quantum state. The proposed circuit generates the superposition of exponentially many Slater determinants, that is, multiconfiguration state, which provides a systematic approach to approximating the exact ground state. We performed the variational quantum eigensolver (VQE) to obtain the ground state of a one-dimensional hydrogen molecular system. As a result, the proposed circuit well reproduced the exact antisymmetric ground state and its energy, whereas the conventional variational circuit yielded neither the antisymmetric nor the symmetric state. Furthermore, we analyzed the many-body wave functions based on the quantum information theory, which illustrated the relation between the electron correlation and the quantum entanglement.

Toward cost-effective quantum circuit simulation with performance tuning techniques

Quantum circuit simulation is a popular approach to evaluating novel quantum algorithms before a physical quantum computer is available. Unfortunately, the simulation is often done with the full-state quantum circuit simulation scheme, and a huge memory space required by a full-state simulator is a limiting factor for the simulation of a larger qubit system. In this work, in order to support the simulation of a broadened qubit system, storage devices are introduced into the full-state quantum circuit simulation. A vertical qubit simulation design is proposed for the storage-based, full-state quantum circuit simulation, including qubit representation, threading model, and parallel state manipulations over storage devices. An empirical method of simulator parameter tuning is developed to achieve higher simulation performance. Our experimental results show that compared with the state-of-the-art memory-only simulator (QuEST), the storage-based simulation can achieve a 61x higher cost-delay ratio and can simulate a 39-qubit system on a commodity computer. The encouraging results indicate that our proposed simulator can help scale the full-state simulation for larger quantum circuits and achieve higher performance via the performance tuning method.

A Setting Optimization Ensemble for a Distributed Power Grid Protective Relay

To ensure a stable and reliable power supply, the valid and timely response of protective relays are indispensable. Through the prevention of fault expansions, potential equipment damage or system collapse can be averted, where their setting is one vital prerequisite for such effective implementations. However, the increasing complexity of distribution power systems results in more challenges for protection tuning strategies. Ergo, this paper presents an ensemble that combines the independent factor evaluation (IFE) and quantum genetic optimization (QGO) models to further optimize the performance of relays according to their distributed tuning environment. In this ensemble, both near and far-end fault characteristics can be incorporated. In the first stage, the IFE dimensional reduction model is deployed for massive heterogeneous input data, where the statistical independence of input signals is calculated, the linear transformation matrix to decouple mixed signals is found, the linear combination of such signals is formed, and the non-Gaussian property to sort them is established. This can ameliorate the following calculation efficiency under those high-dimensional data scenarios. Subsequently, the QGO model is designed to further improve relay settings, where qubit representation is built to reduce required chromosomes, the linear superposition of the optimal solution probability in different states is implemented for a better diversity and convergence performance, and a self-adaption quantum gate is established to dynamically update the qubit chromosome groups and two-state solution combinations. Lastly, an empirical case study is presented, which validates the enhanced convergence, accuracy, and rapidity of the proposed ensemble.

Minimal qubit representations of Hamiltonians via conserved charges

In the last years, we have been witnessing a tremendous push to demonstrate that quantum computers can solve classically intractable problems. This effort, initially focused on the hardware, progressively included the simplification of the models to be simulated. We consider Hamiltonians written in terms of Pauli operators and systematically cut all qubits that are not essential to simulate the system. Our approach is universally applicable and lowers the complexity by first ensuring that the largest possible portion of the Hilbert space becomes irrelevant, and then by finding and exploiting all conserved charges of the system, i.e., symmetries that can be expressed as Pauli operators. Remarkably, both processes are classically efficient and optimal. To showcase our algorithm, we simplify chemical molecules, lattice gauge theories, and the Hubbard and Kitaev models. Published by the American Physical Society 2024

A Novel QKD Approach to Enhance IIOT Privacy and Computational Knacks.

The industry-based internet of things (IIoT) describes how IIoT devices enhance and extend their capabilities for production amenities, security, and efficacy. IIoT establishes an enterprise-to-enterprise setup that means industries have several factories and manufacturing units that are dependent on other sectors for their services and products. In this context, individual industries need to share their information with other external sectors in a shared environment which may not be secure. The capability to examine and inspect such large-scale information and perform analytical protection over the large volumes of personal and organizational information demands authentication and confidentiality so that the total data are not endangered after illegal access by hackers and other unauthorized persons. In parallel, these large volumes of confidential industrial data need to be processed within reasonable time for effective deliverables. Currently, there are many mathematical-based symmetric and asymmetric key cryptographic approaches and identity- and attribute-based public key cryptographic approaches that exist to address the abovementioned concerns and limitations such as computational overheads and taking more time for crucial generation as part of the encipherment and decipherment process for large-scale data privacy and security. In addition, the required key for the encipherment and decipherment process may be generated by a third party which may be compromised and lead to man-in-the-middle attacks, brute force attacks, etc. In parallel, there are some other quantum key distribution approaches available to produce keys for the encipherment and decipherment process without the need for a third party. However, there are still some attacks such as photon number splitting attacks and faked state attacks that may be possible with these existing QKD approaches. The primary motivation of our work is to address and avoid such abovementioned existing problems with better and optimal computational overhead for key generation, encipherment, and the decipherment process compared to the existing conventional models. To overcome the existing problems, we proposed a novel dynamic quantum key distribution (QKD) algorithm for critical public infrastructure, which will secure all cyber–physical systems as part of IIoT. In this paper, we used novel multi-state qubit representation to support enhanced dynamic, chaotic quantum key generation with high efficiency and low computational overhead. Our proposed QKD algorithm can create a chaotic set of qubits that act as a part of session-wise dynamic keys used to encipher the IIoT-based large scales of information for secure communication and distribution of sensitive information.

Scalable qubit representations of neutrino mixing matrices

Oscillating neutrino beams exhibit quantum coherence over distances of thousands of kilometers. Their unambiguously quantum nature suggests an appealing test system for direct quantum simulation. Such techniques may enable presently analytically intractable calculations involving multi-neutrino entanglements, such as collective neutrino oscillations in supernovae, but only once oscillation phenomenology is properly re-expressed in the language of quantum circuits. Here we resolve outstanding conceptual issues regarding encoding of arbitrarily mixed neutrino flavor states in the Hilbert space of an n-qubit quantum computer. We introduce algorithms to encode mixing and oscillation of any number of flavor-mixed neutrinos, both with and without CP-violation, with an efficient number of prescriptive input parameters in terms of sub-rotations of the PMNS matrix in standard form. Examples encoded for an IBM-Q quantum computer are shown to converge to analytic predictions both with and without CP-violation.

Hierarchical qubit maps and hierarchically implemented quantum error correction

We consider hierarchically implemented quantum error correction (HI-QEC), in which the fidelities of logical qubits are differentially optimized to enhance the capabilities of quantum devices in scientific applications. By employing qubit representations that propagate hierarchies in simulated systems to those in logical qubit noise sensitivities, heterogeneity in the distribution of physical-to-logical qubits can be systematically structured. For concreteness, we estimate HI-QEC's impact on surface code resources in computing low-energy observables to fixed precision, finding up to $\sim 60\%$ reductions in qubit requirements plausible in early error corrected simulations. Hierarchical qubit maps are also possible without error correction in qubit and qudit systems where fidelities are non-uniform, either unintentionally or by design. Hierarchical optimizations are another element in the co-design process of quantum simulations for nuclear and particle physics.

Quantum simulation of molecules without fermionic encoding of the wave function

Molecular simulations generally require fermionic encoding in which fermion statistics are encoded into the qubit representation of the wave function. Recent calculations suggest that fermionic encoding of the wave function can be bypassed, leading to more efficient quantum computations. Here we show that the two-electron reduced density matrix (2-RDM) can be expressed as a unique functional of the unencoded N-qubit-particle wave function without approximation, and hence, the energy can be expressed as a functional of the 2-RDM without fermionic encoding of the wave function. In contrast to current hardware-efficient methods, the derived functional has a unique, one-to-one (and onto) mapping between the qubit-particle wave functions and 2-RDMs, which avoids the over-parametrization that can lead to optimization difficulties such as barren plateaus. An application to computing the ground-state energy and 2-RDM of H4 is presented.

One- and two-dimensional quantum lattice algorithms for Maxwell equations in inhomogeneous scalar dielectric media I: theory

ABSTRACT A quantum lattice algorithm (QLA) is developed for Maxwell equations in scalar dielectric media using the Riemann–Silberstein representation on a Cartesian grid. For x-dependent and y-dependent dielectric inhomogeneities, the corresponding QLA requires a minimum of 8 qubits/spatial lattice site. This is because the corresponding Pauli spin matrices have off-diagonal components which permit the local collisional entanglement of these qubits. However, z-dependent inhomogeneities require a QLA with a minimum of 16 qubits/lattice site since the Pauli spin matrix is diagonal. For two-dimensional inhomogeneities, one can readily couple the 8–8 qubit schemes for x−y variations. z−x and y−z variations can be treated by either a 16–8 qubit scheme or a 16–16 qubit representation.

Reducing Qubit Requirements for Quantum Simulations Using Molecular Point Group Symmetries

Simulating molecules is believed to be one of the early stage applications for quantum computers. Current state-of-the-art quantum computers are limited in size and coherence; therefore, optimizing resources to execute quantum algorithms is crucial. In this work, we develop the second quantization representation of spatial symmetries, which are then transformed to their qubit operator representation. These qubit operator representations are used to reduce the number of qubits required for simulating molecules. We present our results for various molecules and elucidate a formal connection of this work with a previous technique that analyzed generic Z2 Pauli symmetries.

New look on quantum representation of images: Fourier transform representation

Image representation plays an essential role in quantum image processing and quantum computer vision in numerous, computationally expensive applications. Quantum image processing is a new discipline with tremendous potential. However, there is a critical problem in applying quantum computing to process data: how to represent data (signal, image, and video data) using quantum states without losing information. In this paper, we describe briefly a few known models for image representation and propose a new approach for representing discrete signals and images in quantum computing, by mapping the input data into the unit circle, or only part of the circle. Such a representation allows for introducing the concept of the Fourier transform qubit representation. For grayscale images, we consider the similar concept of the Fourier representation of images and, for color images, we introduce models with the concept of the 3-point DFT of color qubits. The circuits for proposed signal and image representations are described.

Real-time simulation of flux qubits used for quantum annealing

The real-time flux dynamics of up to three superconducting quantum interference devices (SQUIDs) are studied by numerically solving the time-dependent Schr\"odinger equation. The numerical results are used to scrutinize the mapping of the flux degrees of freedom onto two-level systems (the qubits) as well as the performance of the intermediate SQUID as a tunable coupling element. It is shown that the qubit representation yields a good description of the flux dynamics during quantum annealing and the presence of the tunable coupling element does not have negative effects on the overall performance. Additionally, data obtained from a simulation of the dynamics of two-level systems during quantum annealing are compared to experimental data produced by the D-Wave 2000Q quantum annealer. The effects of finite temperature are incorporated in the simulation by coupling the qubit system to a bath of two-level systems. It is shown that an environment modeled as non-interacting two-level systems coupled to the qubits can produce data which matches the experimental data much better than the simulation data of the qubits without coupling to an environment and better than data obtained from a simulation of an environment modeled as interacting two-level systems coupling to the qubits.

Increasing the Representation Accuracy of Quantum Simulations of Chemistry without Extra Quantum Resources

Proposals for near-term experiments in quantum chemistry on quantum computers leverage the ability to target a subset of degrees of freedom containing the essential quantum behavior, sometimes called the active space. This approximation allows one to treat more difficult problems using fewer qubits and lower gate depths than would otherwise be possible. However, while this approximation captures many important qualitative features, it may leave the results wanting in terms of absolute accuracy (basis error) of the representation. In traditional approaches, increasing this accuracy requires increasing the number of qubits and an appropriate increase in circuit depth as well. Here we introduce a technique requiring no additional qubits or circuit depth that is able to remove much of this approximation in favor of additional measurements. The technique is constructed and analyzed theoretically, and some numerical proof of concept calculations are shown. As an example, we show how to achieve the accuracy of a 20 qubit representation using only 4 qubits and a modest number of additional measurements for a simple hydrogen molecule. We close with an outlook on the impact this technique may have on both near-term and fault-tolerant quantum simulations.

Qubit representation of qudit states: correlations and state reconstruction

A method to establish a qubit decomposition of a general qudit state is presented. This new representation allows a geometrical depiction of any qudit state in the Bloch sphere. Additionally, we show that the nonnegativity conditions of the qudit state imply the existence of quantum correlations between the qubits which compose it. These correlations are used to define new inequalities which the density matrices components must satisfy. The importance of such inequalities in the reconstruction of a qudit state is addressed. As an example of the general procedure the qubit decomposition of a qutrit system is shown, which allows a classification of the qutrit states by fixing their invariants ${\rm Tr}(\hat{\rho}^2)$, ${\rm Tr}(\hat{\rho}^3)$.

Memristive Quantum Computing Simulator

One of the most promising and powerful candidates for future computing is the notion of universal quantum computer. A vital advance towards this direction is the development of quantum simulators and their possible implementation either as standalone quantum systems or as compatible software for classical computers with pros and cons. On the other hand, memristive computing has been proposed recently as a tentative unconventional computing scheme promoting the idea of information storage and processing in the same nanoelectronic device. In this paper we present a memristive quantum computing simulator by coupling quantum simulation principles with memristor aspects and enabling us to tackle the existing difficulties on qubit representation in conventional computing systems. For doing so, we utilize the memristances of identical memristors to represent in 3D the qubit state while its corresponding evolution is defined by the memristors input voltages. In particular, we introduce an appropriate correspondence among the aforementioned memristor voltages and the general qubit state rotation, i.e., the one-qubit quantum gates, and as such we reproduce the rotations imposed by the action of quantum gates in the 3D memristance space. Moreover, we also define the action of the CNOT two-qubit gate and simulate entanglement between two qubits paving the way towards the establishment of a universal set for quantum computing. Our results show that, memristor circuits can simulate effectively quantum computations.

Electron-Phonon Systems on a Universal Quantum Computer.

We present an algorithm that extends existing quantum algorithms for simulating fermion systems in quantum chemistry and condensed matter physics to include bosons in general and phonons in particular. We introduce a qubit representation for the low-energy subspace of phonons which allows an efficient simulation of the evolution operator of the electron-phonon systems. As a consequence of the Nyquist-Shannon sampling theorem, the phonons are represented with exponential accuracy on a discretized Hilbert space with a size that increases linearly with the cutoff of the maximum phonon number. The additional number of qubits required by the presence of phonons scales linearly with the size of the system. The additional circuit depth is constant for systems with finite-range electron-phonon and phonon-phonon interactions and linear for long-range electron-phonon interactions. Our algorithm for a Holstein polaron problem was implemented on an Atos quantum learning machine quantum simulator employing the quantum phase estimation method. The energy and the phonon number distribution of the polaron state agree with exact diagonalization results for weak, intermediate, and strong electron-phonon coupling regimes.

A programmable two-qubit quantum processor in silicon

Now that it is possible to achieve measurement and control fidelities for individual quantum bits (qubits) above the threshold for fault tolerance, attention is moving towards the difficult task of scaling up the number of physical qubits to the large numbers that are needed for fault-tolerant quantum computing. In this context, quantum-dot-based spin qubits could have substantial advantages over other types of qubit owing to their potential for all-electrical operation and ability to be integrated at high density onto an industrial platform. Initialization, readout and single- and two-qubit gates have been demonstrated in various quantum-dot-based qubit representations. However, as seen with small-scale demonstrations of quantum computers using other types of qubit, combining these elements leads to challenges related to qubit crosstalk, state leakage, calibration and control hardware. Here we overcome these challenges by using carefully designed control techniques to demonstrate a programmable two-qubit quantum processor in a silicon device that can perform the Deutsch-Josza algorithm and the Grover search algorithm-canonical examples of quantum algorithms that outperform their classical analogues. We characterize the entanglement in our processor by using quantum-state tomography of Bell states, measuring state fidelities of 85-89 per cent and concurrences of 73-82 per cent. These results pave the way for larger-scale quantum computers that use spins confined to quantum dots.

Fusion method for infrared and visible images based on improved quantum theory model

Quantum theory model (QTM) owns a superior characteristic to turn a complex problem into the form of the linear combination of several much simpler components. Therefore, a novel fusion method based on improved quantum theory model (IQTM) is proposed in this paper, aiming at dealing with the fusion problem of infrared and visible images. Firstly, the traditional QTM is modified to be a better version called IQTM. Compared with the traditional QTM, IQTM has three qubit states responsible for reflecting much more information of the represented pixel in the image. Then, the pixels of the source images are transformed into the qubit state representation, and the corresponding quantum results can be obtained according to the basic principle of quantum theory. Finally, the quantum results are transformed into the final fused image. Experimental results show that the proposed method has remarked superiorities over other current typical ones in terms of both fusion performance and computational efficiency.

Qubit representations of the braid groups from generalized Yang–Baxter matrices

Generalized Yang---Baxter matrices sometimes give rise to braid group representations. We identify the exact images of some qubit representations of the braid groups from generalized Yang---Baxter matrices obtained from anyons in the metaplectic modular categories.

Quantum inspired cuckoo search algorithm for graph colouring problem

The graph colouring problem GCP is one of the most interesting, studied and difficult combinatorial optimisation problems. That is why, several approaches were developed for solving this problem, including exact approaches, heuristic approaches, metaheuristics and hybrid approaches. In this paper, we try to solve the graph colouring problem using a new approach based on the quantum inspired cuckoo search algorithm. The first contribution consists in defining an appropriate quantum representation based on qubit representation to represent the graph colouring solutions. The second contribution is the proposition of a novel measure operator based on the adjacency matrix. The third contribution involves the proposition of an adapted hybrid quantum mutation operation. To show the feasibility and the effectiveness of the algorithm, we have used the standard DIMACS benchmark, and the obtained results are very encouraging.