Number Of Available Qubits Research Articles

Benchmarking Multipartite Entanglement Generation with Graph States

AbstractAs quantum computing technology slowly matures and the number of available qubits on a QPU gradually increases, interest in assessing the capabilities of quantum computing hardware in a scalable manner is growing. One of the key properties for quantum computing is the ability to generate multipartite entangled states. In this study, aspects of benchmarking entanglement generation capabilities of noisy intermediate‐scale quantum (NISQ) devices are discussed based on the preparation of graph states and the verification of entanglement in the prepared states. Thereby, entanglement witnesses that are specifically suited for a scalable experiment design are used. This choice of entanglement witnesses can detect A) bipartite entanglement and B) genuine multipartite entanglement for graph states with constant two measurement settings if the prepared graph state is based on a two‐colorable graph, e.g., a square grid graph or one of its subgraphs. With this, it is experimentally verified that a bipartite entangled state comprising all qubits can be prepared on a 127‐qubit IBM Quantum superconducting QPU, and genuine multipartite entanglement can be detected for states of up to 23 qubits with quantum readout error mitigation.

DECENTRALIZED QUANTUM COMPILATION FRAMEWORK: EMPOWERING DISTRIBUTED QUANTUM COMPUTING THROUGH MODULARITY

Quantum algorithms require large resources in terms of qubit number, much larger than those available with current NISQ processors. With the network and communication functionalities provided by the Quantum Internet, Distributed Quantum Computing (DQC) is considered as a scalable approach for increasing the number of available qubits for computational tasks. For DQC to be effective and efficient, a quantum compiler must find the best partitioning for the quantum algorithm and then perform smart remote operation scheduling to optimize EPR pair consumption. At the same time, the quantum compiler should also find the best local transformation for each partition. In this paper we present a modular quantum compilation framework for DQC that takes into account both network and device constraints and characteristics. We implemented and tested a quantum compiler based on the proposed framework with some circuits of interest, such as the VQE and QFT ones, considering different network topologies, with quantum processors characterized by heavy hexagon coupling maps. We also devised a strategy for remote scheduling that can exploit both TeleGate and TeleData operations and tested the impact of using either only TeleGates or both. The evaluation results show that TeleData operations may have a positive impact on the number of consumed EPR pairs, while choosing a more connected network topology helps reduce the number of layers dedicated to remote operations. Keywords— Distributed quantum computing (DQC), quantum compilation, quantum Internet

Quantum annealing-based computed tomography using variational approach for a real-number image reconstruction

Objective. Despite recent advancements in quantum computing, the limited number of available qubits has hindered progress in CT reconstruction. This study investigates the feasibility of utilizing quantum annealing-based computed tomography (QACT) with current quantum bit levels. Approach. The QACT algorithm aims to precisely solve quadratic unconstrained binary optimization problems. Furthermore, a novel approach is proposed to reconstruct images by approximating real numbers using the variational method. This approach allows for accurate CT image reconstruction using a small number of qubits. The study examines the impact of projection data quantity and noise on various image sizes ranging from 4 × 4 to 24 × 24 pixels. The reconstructed results are compared against conventional reconstruction algorithms, namely maximum likelihood expectation maximization (MLEM) and filtered back projection (FBP). Main result. By employing the variational approach and utilizing two qubits for each pixel of the image, accurate reconstruction was achieved with an adequate number of projections. Under conditions of abundant projections and lower noise levels, the image quality in QACT algorithm outperformed that of MLEM and FBP algorithms. However, in situations with limited projection data and in the presence of noise, the image quality in QACT was inferior to that in MLEM. Significance. This study developed the QACT reconstruction algorithm using the variational approach for real-number reconstruction. Remarkably, only 2 qubits were required for each pixel representation, demonstrating their sufficiency for accurate reconstruction.

Improving Noisy Hybrid Quantum Graph Neural Networks for Particle Decay Tree Reconstruction

Improving Noisy Hybrid Quantum Graph Neural Networks for Particle Decay Tree Reconstruction

Quantum gate algorithm for reference-guided DNA sequence alignment

Reference-guided DNA sequencing and alignment is an important process in computational molecular biology. The amount of DNA data grows very fast, and many new genomes are waiting to be sequenced while millions of private genomes need to be re-sequenced. Each human genome has 3.2B base pairs, and each one could be stored with 2 bits of information, so one human genome would take 6.4B bits or ∼760MB of storage (National Institute of General Medical Sciences, n.d.). Today’s most powerful tensor processing units cannot handle the volume of DNA data necessitating a major leap in computing power. It is, therefore, important to investigate the usefulness of quantum computers in genomic data analysis, especially in DNA sequence alignment. Quantum computers are expected to be involved in DNA sequencing, initially as parts of classical systems, acting as quantum accelerators. The number of available qubits is increasing annually, and future quantum computers could conduct DNA sequencing, taking the place of classical computing systems. We present a novel quantum algorithm for reference-guided DNA sequence alignment modeled with gate-based quantum computing. The algorithm is scalable, can be integrated into existing classical DNA sequencing systems and is intentionally structured to limit computational errors. The quantum algorithm has been tested using the quantum processing units and simulators provided by IBM Quantum, and its correctness has been confirmed.

A quantum circuit to generate random numbers within a specific interval

Random numbers are of vital importance in fields such as cyptography and scientific simulations. However, it is well known how difficult it is for classical computers to generate random numbers. This is not the case for quantum computers, which are able to genuinely generate random numbers thanks to the property of superposition and their counter-intuitive concept of measurement. However, despite the simplicity of designing a circuit that generates a random number between 0 and 2^{N}-1 (being N the number of available qubits), designing a quantum circuit to generate a number within a specific interval is far from trivial. This paper proposes a customizable circuit design to generate random numbers. The circuit is non- hardware dependent, it allows fault-tolerance, and it can be used by current quantum devices. Therefore, it is a valuable tool for all those quantum applications and algorithms that need to work with random numbers. Moreover, a comparator circuit has also been designed as part of this work. This comparator is the best currently available in the literature in terms of qubits, T-count, and T-depth. It is therefore a useful tool for any other circuit or algorithm where this operation is needed.

Using Variational Quantum Algorithm to Solve the LWE Problem

The variational quantum algorithm (VQA) is a hybrid classical–quantum algorithm. It can actually run in an intermediate-scale quantum device where the number of available qubits is too limited to perform quantum error correction, so it is one of the most promising quantum algorithms in the noisy intermediate-scale quantum era. In this paper, two ideas for solving the learning with errors problem (LWE) using VQA are proposed. First, after reducing the LWE problem into the bounded distance decoding problem, the quantum approximation optimization algorithm (QAOA) is introduced to improve classical methods. Second, after the LWE problem is reduced into the unique shortest vector problem, the variational quantum eigensolver (VQE) is used to solve it, and the number of qubits required is calculated in detail. Small-scale experiments are carried out for the two LWE variational quantum algorithms, and the experiments show that VQA improves the quality of the classical solutions.

A hybrid algorithm framework for small quantum computers with application to finding Hamiltonian cycles

Recent works have shown that quantum computers can polynomially speed up certain SAT-solving algorithms even when the number of available qubits is significantly smaller than the number of variables. Here, we generalize this approach. We present a framework for hybrid quantum-classical algorithms which utilize quantum computers significantly smaller than the problem size. Given an arbitrarily small ratio of the quantum computer to the instance size, we achieve polynomial speedups for classical divide-and-conquer algorithms, provided that certain criteria on the time- and space-efficiency are met. We demonstrate how this approach can be used to enhance Eppstein’s algorithm for the cubic Hamiltonian cycle problem and achieve a polynomial speedup for any ratio of the number of qubits to the size of the graph.

Improving solutions by embedding larger subproblems in a D-Wave quantum annealer

Quantum annealing is a heuristic algorithm that solves combinatorial optimization problems, and D-Wave Systems Inc. has developed hardware implementation of this algorithm. However, in general, we cannot embed all the logical variables of a large-scale problem, since the number of available qubits is limited. In order to handle a large problem, qbsolv has been proposed as a method for partitioning the original large problem into subproblems that are embeddable in the D-Wave quantum annealer, and it then iteratively optimizes the subproblems using the quantum annealer. Multiple logical variables in the subproblem are simultaneously updated in this iterative solver, and using this approach we expect to obtain better solutions than can be obtained by conventional local search algorithms. Although embedding of large subproblems is essential for improving the accuracy of solutions in this scheme, the size of the subproblems are small in qbsolv since the subproblems are basically embedded by using an embedding of a complete graph even for sparse problem graphs. This means that the resource of the D-Wave quantum annealer is not exploited efficiently. In this paper, we propose a fast algorithm for embedding larger subproblems, and we show that better solutions are obtained efficiently by embedding larger subproblems.

Quantum Annealing for Prime Factorization

We have developed a framework to convert an arbitrary integer factorization problem to an executable Ising model by first writing it as an optimization function then transforming the k-bit coupling (k ≥ 3) terms to quadratic terms using ancillary variables. Our resource-efficient method uses {mathscr{O}}({mathrm{log}}^{2}(N)) binary variables (qubits) for finding the factors of an integer N. We present how to factorize 15, 143, 59989, and 376289 using 4, 12, 59, and 94 logical qubits, respectively. This method was tested using the D-Wave 2000Q for finding an embedding and determining the prime factors for a given composite number. The method is general and could be used to factor larger integers as the number of available qubits increases, or combined with other ad hoc methods to achieve better performances for specific numbers.

Quantum computation and quantum simulation

In past few years, quantum computation and quantum simulation have been developed rapidly. The research on quantum computation and quantum simulation involving medium scale number of qubits will have a development priority. In this paper, we review recent developments in those directions. The review will include quantum simulation of many-body system, quantum computation, digital quantum simulators and cloud quantum computation platforms, and quantum software. The quantum simulation of many-body system will include the simulation of quantum dynamics, time crystal and many-body localization, quantum statistical physics and quantum chemistry. The review of those results is based on our consideration to the current characteristics of quantum computation and quantum simulation. Specifically, the number of available qubits is on a medium scale from dozens to several hundreds, the fidelity of the quantum logic gate is not high enough for several thousand of operations. In this sense, the present research is at the stage from fundamental explorations to practical applications. With these in mind, we hope that this review can be helpful for the future study in quantum computation and quantum simulation.

Experiments of quantum nonlocality with polarization-momentum entangled photon pairs

We present the results of some experimental tests of quantum nonlocality performed by two-photon states, entangled both in polarization and momentum, namely hyperentangled states and two-photon four-qubit linear cluster states. These states, which double the number of available qubits with respect to the standard two-photon entangled states, are engineered by a simple experimental method, which adopts linear optics and a single type I nonlinear crystal. The tests of local realism performed with these states represent a generalization of the Greenberger, Home, and Zeilinger (GHZ) theorem to the case of two entangled particles.

Subsystem pseudopure states

A critical step in experimental quantum information processing (QIP) is to implement control of quantum systems protected against decoherence via informational encodings, such as quantum error correcting codes, noiseless subsystems and decoherence free subspaces. These encodings lead to the promise of fault tolerant QIP, but they come at the expense of resource overheads. Part of the challenge in studying control over multiple logical qubits, is that QIP test-beds have not had sufficient resources to analyze encodings beyond the simplest ones. The most relevant resources are the number of available qubits and the cost to initialize and control them. Here we demonstrate an encoding of logical information that permits the control over multiple logical qubits without full initialization, an issue that is particularly challenging in liquid state NMR. The method of subsystem pseudo-pure state will allow the study of decoherence control schemes on up to 6 logical qubits using liquid state NMR implementations.

NMR quantum computing: applying theoretical methods to designing enhanced systems.

Density functional theory results for chemical shifts and spin-spin coupling constants are presented for compounds currently used in NMR quantum computing experiments. Specific design criteria were examined and numerical guidelines were assessed. Using a field strength of 7.0 T, protons require a coupling constant of 4 Hz with a chemical shift separation of 0.3 ppm, whereas carbon needs a coupling constant of 25 Hz for a chemical shift difference of 10 ppm, based on the minimal coupling approximation. Using these guidelines, it was determined that 2,3-dibromothiophene is limited to only two qubits; the three qubit system bromotrifluoroethene could be expanded to five qubits and the three qubit system 2,3-dibromopropanoic acid could also be used as a six qubit system. An examination of substituent effects showed that judiciously choosing specific groups could increase the number of available qubits by removing rotational degeneracies in addition to introducing specific conformational preferences that could increase (or decrease) the magnitude of the couplings. The introduction of one site of unsaturation can lead to a marked improvement in spectroscopic properties, even increasing the number of active nuclei.