Towards Compact Modeling of Noisy Quantum Computers: A Molecular-Spin-Qubit Case of Study

Classical simulation of Noisy Intermediate Scale Quantum computers is a crucial task for testing the expected performance of real hardware. The standard approach, based on solving Schrödinger and Lindblad equations, is demanding when scaling the number of qubits in terms of both execution time and memory. In this article, attempts in defining compact models for the simulation of quantum hardware are proposed, ensuring results close to those obtained with standard formalism. Molecular Nuclear Magnetic Resonance quantum hardware is the target technology, where three non-ideality phenomena—common to other quantum technologies—are taken into account: decoherence, off-resonance qubit evolution, and undesired qubit-qubit residual interaction. A model for each non-ideality phenomenon is embedded into a MATLAB simulation infrastructure of noisy quantum computers. The accuracy of the models is tested on a benchmark of quantum circuits, in the expected operating ranges of quantum hardware. The corresponding outcomes are compared with those obtained via numeric integration of the Schrödinger equation and the Qiskit’s QASMSimulator. The achieved results give evidence that this work is a step forward towards the definition of compact models able to provide fast results close to those obtained with the traditional physical simulation strategies, thus paving the way for their integration into a classical simulator of quantum computers.

Twist: sound reasoning for purity and entanglement in Quantum programs

Quantum programming languages enable developers to implement algorithms for quantum computers that promise computational breakthroughs in classically intractable tasks. Programming quantum computers requires awareness of entanglement , the phenomenon in which measurement outcomes of qubits are correlated. Entanglement can determine the correctness of algorithms and suitability of programming patterns. In this work, we formalize purity as a central tool for automating reasoning about entanglement in quantum programs. A pure expression is one whose evaluation is unaffected by the measurement outcomes of qubits that it does not own, implying freedom from entanglement with any other expression in the computation. We present Twist, the first language that features a type system for sound reasoning about purity. The type system enables the developer to identify pure expressions using type annotations. Twist also features purity assertion operators that state the absence of entanglement in the output of quantum gates. To soundly check these assertions, Twist uses a combination of static analysis and runtime verification. We evaluate Twist’s type system and analyses on a benchmark suite of quantum programs in simulation, demonstrating that Twist can express quantum algorithms, catch programming errors in them, and support programs that existing languages disallow, while incurring runtime verification overhead of less than 3.5%.

Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds

Here we report a breakthrough in the fabrication of a long lifetime transmon qubit. We use tantalum films as the base superconductor. By using a dry etching process, we obtained transmon qubits with a best T1 lifetime of 503 μs. As a comparison, we also fabricated transmon qubits with other popular materials, including niobium and aluminum, under the same design and fabrication processes. After characterizing their coherence properties, we found that qubits prepared with tantalum films have the best performance. Since the dry etching process is stable and highly anisotropic, it is much more suitable for fabricating complex scalable quantum circuits, when compared to wet etching. As a result, the current breakthrough indicates that the dry etching process of tantalum film is a promising approach to fabricate medium- or large-scale superconducting quantum circuits with a much longer lifetime, meeting the requirements for building practical quantum computers.

Efficient Decomposition of Unitary Matrices in Quantum Circuit Compilers

Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for the translation of bigger unitary gates into elementary quantum operations, which is key to executing these algorithms on existing quantum computers. The decomposition can be used as an aggressive optimization method for the whole circuit, as well as to test part of an algorithm on a quantum accelerator. For the selection and implementation of the decomposition algorithm, perfect qubits are assumed. We base our decomposition technique on Quantum Shannon Decomposition, which generates O(344n) controlled-not gates for an n-qubit input gate. In addition, we implement optimizations to take advantage of the potential underlying structure in the input or intermediate matrices, as well as to minimize the execution time of the decomposition. Comparing our implementation to Qubiter and the UniversalQCompiler (UQC), we show that our implementation generates circuits that are much shorter than those of Qubiter and not much longer than the UQC. At the same time, it is also up to 10 times as fast as Qubiter and about 500 times as fast as the UQC.

A Comparative Study of Post-Quantum Cryptosystems for Internet-of-Things Applications

The existence of quantum computers and Shor’s algorithm poses an imminent threat to classical public-key cryptosystems. These cryptosystems are currently used for the exchange of keys between servers and clients over the Internet. The Internet of Things (IoT) is the next step in the evolution of the Internet, and it involves the connection of millions of low-powered and resource-constrained devices to the network. Because quantum computers are becoming more capable, the creation of a new cryptographic standard that cannot be compromised by them is indispensable. There are several current proposals of quantum-resistant or post-quantum algorithms that are being considered for future standards. Given that the IoT is increasing in popularity, and given its resource-constrained nature, it is worth adapting those new standards to IoT devices. In this work, we study some post-quantum cryptosystems that could be suitable for IoT devices, adapting them to work with current cryptography and communication software, and conduct a performance measurement on them, obtaining guidelines for selecting the best for different applications in resource-constrained hardware. Our results show that many of these algorithms can be efficiently executed in current IoT hardware, providing adequate protection from the attacks that quantum computers will eventually be capable of.

VQE method: a short survey and recent developments

The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such as quantum phase estimation (QPE) because fully quantum algorithms require quantum hardware that will not be accessible in the near future. VQE has been successfully applied to solve the electronic Schrödinger equation for a variety of small molecules. However, the scalability of this method is limited by two factors: the complexity of the quantum circuits and the complexity of the classical optimization problem. Both of these factors are affected by the choice of the variational ansatz used to represent the trial wave function. Hence, the construction of an efficient ansatz is an active area of research. Put another way, modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatzes for problems that map onto more than several qubits. In this review, we present recent developments in the field of designing efficient ansatzes that fall into two categories—chemistry–inspired and hardware–efficient—that produce quantum circuits that are easier to run on modern hardware. We discuss the shortfalls of ansatzes originally formulated for VQE simulations, how they are addressed in more sophisticated methods, and the potential ways for further improvements.

QUBO Formulations for a System of Linear Equations

With the advent of quantum computers, many quantum computing algorithms are being developed. Solving linear systems is one of the most fundamental problems in almost all of science and engineering. Harrow-Hassidim-Lloyd algorithm, a monumental quantum algorithm for solving linear systems on the gate model quantum computers, was invented and several advanced variations have been developed. For a given square matrix A∈R(n×n) and a vector b∈R(n), we will find unconstrained binary optimization (QUBO) models for a vector x∈R(n) that satisfies Ax=b. To formulate QUBO models for a linear system solving problem, we make use of a linear least-square problem with binary representation of the solution. We validate those QUBO models on the D-Wave system and discuss the results. For a simple system, We provide a python code to calculate the matrix characterizing the relationship between the variables and to print the test code that can be used directly in D-Wave system.

QNet: A Scalable and Noise-Resilient Quantum Neural Network Architecture for Noisy Intermediate-Scale Quantum Computers

Quantum machine learning (QML) is promising for potential speedups and improvements in conventional machine learning (ML) tasks. Existing QML models that use deep parametric quantum circuits (PQC) suffer from a large accumulation of gate errors and decoherence. To circumvent this issue, we propose a new QML architecture called QNet. QNet consists of several small quantum neural networks (QNN). Each of these smaller QNN’s can be executed on small quantum computers that dominate the NISQ-era machines. By carefully choosing the size of these QNN’s, QNet can exploit arbitrary size quantum computers to solve supervised ML tasks of any scale. It also enables heterogeneous technology integration in a single QML application. Through empirical studies, we show the trainability and generalization of QNet and the impact of various configurable variables on its performance. We compare QNet performance against existing models and discuss potential issues and design considerations. In our study, we show 43% better accuracy on average over the existing models on noisy quantum hardware emulators. More importantly, QNet provides a blueprint to build noise-resilient QML models with a collection of small quantum neural networks with near-term noisy quantum devices.