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.
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.
The new quantum era is expected to have an unprecedented social impact, enabling the research of tomorrow in several pivotal fields. These perspectives require a physical system able to encode, process and store for a sufficiently long amount of time the quantum information. However, the optimal engineering of currently available quantum computers, which are small and flawed by several non-ideal phenomena, requires an efficacious methodology for exploring the design space. Hence, there is an unmet need for the development of reliable hardware-aware simulation infrastructures able to efficiently emulate the behaviour of quantum hardware that commits to looking for innovative systematic ways, with a bottom-up approach starting from the physical level, moving to the device level and up to the system level. This article discusses the development of a classical simulation infrastructure for semiconductor quantum-dot quantum computation based on compact models, where each device is described in terms of the main physical parameters affecting its performance in a sufficiently easy way from a computational point of view for providing accurate results without involving sophisticated physical simulators, thus reducing the requirements on CPU and memory. The effectiveness of the involved approximations is tested on a benchmark of quantum circuits — in the expected operating ranges of quantum hardware — by comparing the corresponding outcomes with those obtained via numeric integration of the Schrödinger equation. The achieved results give evidence that this work is a step forward towards the definition of a classical simulator of quantum computers.
Molecules are serious candidates for building hardware for quantum computers. They can encode quantum information onto electron or nuclear spins and some of them show important features as the scalability of the number of qubits and a universal set of quantum gates. In this paper we present our advances in the development of a classical simulation infrastructure for molecular Quantum Computing: starting from the definition of simplified models taking into account the main physical features of each analyzed molecule, quantum gates are defined over these models, thus permitting to take into account the real behavior of each technology during the simulation. An interface with a hardware-agnostic description language has been also developed. The knowledge of the behavior of real systems permits to optimize the design of quantum circuits at both physical and compilation levels. Elementary quantum algorithms have been simulated on three different molecular technologies by changing the physical parameters of polarization and manipulation and quantum circuit design strategies. Results confirm the dependency of the fidelity of the results on both levels, thus proving that the choice of optimal operating points and circuit optimization techniques as virtual-Z gates are fundamental for ensuring the execution of quantum circuits with negligible errors.
Standard CMOS circuits are expected to be no longer able to satisfy nowadays demand for higher performances and lower power consumption. This commits to look for new solutions. Quantum computation, whose fundamental quantity of information is the qubit, is a thoroughly new way of thinking to electronics. There are at least two main reasons for which quantum computing is expected to broaden computation horizons. First, specific algorithms can be engineered, manipulating the probability amplitudes of different states, to exploit the quantum superposition principle and achieve high parallelism. Second, it is expected to be spontaneously suitable to simulate complex quantum physical systems, as large molecules. Quantum computing requires the cooperation of several scientific fields. The leading idea has been to highlight the operations and algorithms a quantum computer must be able to perform and, then, to propose a hardware solution, providing the rigorous physical treatment mandatory for a deep understanding and for an appropriate modelling, something which is hard to find in nowadays literature. Thus, the first chapters address the quantum algorithms, focusing on Grover's search algorithm and deriving, from fundamentals, the corresponding circuit. The latter is then described in Quantum Assembly (QASM), which can be seen as the quantum equivalent of VHDL, and simulated on IBM Q Experience. The following chapters deal with a possible physical implementation of quantum processors: the encoding of qubits on nuclear spins in diamagnetic molecules. When a static magnetic field is applied to a spin-1/2 nucleus, two well-defined energy eigenstates arise, as a result of the Zeeman effect. Each of them can be associated with a qubit eigenstate. Thanks to nuclear magnetic resonance principles, the probability with which one of the two eigenstates is measured can be handled by the superposition of a radio frequency field at the resonance frequency of the nucleus. This can be interpreted as a rotation of the spin, and so of the qubit, about the RF field and enables the execution of single qubit quantum gates, since they are simple rotations of the state vector. The two-qubit CNOT gate is obtained through the interaction of spins via J-coupling. Considering that these gates constitute a universal set, every quantum algorithm can theoretically be run on an NMR processor. Different nuclei have different resonant frequencies, but the addressing of a specific spin can be achieved also in homonuclear molecules, since the resonant frequency depends also on the nuclear environment (nuclear shielding). While unwanted J-couplings can be removed thanks to refocusing, spin decoherence and relaxation phenomena force an upper limit to the allowed timescale. A main advantage of NMR is that this timescale is long, even at room temperature. Conversely, scalability is still an issue. A simple heteronuclear MATLAB model, based on the relations derived from first principles in the thesis, is proposed to prove the feasibility of NMR quantum processors. The input technological parameters, as chemical shielding and J-coupling, can be computed resorting on ORCA, or obtained from experimental data. The model, able to run a universal set of quantum gates and simple algorithms, can be useful to find an optimal operating point as a compromise between molecule physical properties and the quantities which can be controlled by nowadays NMR instrumentation.
With the latest advances in quantum computing technology, we are gradually moving from the noisy intermediate-scale quantum (NISQ) era characterized by hardware limited in the number of qubits and plagued with quantum noise, to the age of quantum utility where both the newest hardware and software methods allow for tackling problems which have been deemed difficult or intractable with conventional classical methods. One of these difficult problems is the simulation of one-dimensional (1D) nuclear magnetic resonance (NMR) spectra, a major tool to learn about the structure of molecules, helping the design of new materials or drugs. Using advanced error mitigation and error suppression techniques from Q-CTRL together with the latest commercially available superconducting-qubit quantum computer from IBM and trapped-ion quantum computer from IonQ, we present the quantum Hamiltonian simulation of liquid-state 1D NMR spectra in the high-field regime for spin systems up to 34 spins. Our pipeline has a major impact on the ability to execute deep quantum circuits with the reduction of quantum noise, improving mean square error by a factor of 22. It allows for the execution of deep quantum circuits and obtaining salient features of the 1D NMR spectra for both 16-spin and 22-spin systems, as well as a 34-spin system, which lies beyond the regime where unrestricted full Liouvillespace simulations are practical (32 spins, the Liouville limit). Our work is a step toward near-term quantum utility in NMR spectroscopy.
Molecular nanomagnets can be considered as serious candidates for the definition of a scalable and reliable quantum computing technology: information is encoded on their spins and they ensure relaxation and decoherence times sufficiently long for the execution of tens of quantum operations. Among these devices, Cr7Ni supramolecular complexes are extremely of interest since they implement a universal set of quantum gates, made of single-qubit gates and the two-qubit Controlled-phase gate. A model for analyzing Cr7Ni molecules and a potential quantum computer architecture are proposed: starting from the energy parameters required for spin manipulations, these systems have been proved to implement elementary quantum algorithms. Within this paper, two, three and four-qubit systems have been analyzed: the simulation of quantum operations and the analysis of dynamical non-idealities have been done in parallel. Our approach enables the definition of an operating point - in terms of magnetic driving fields and latency - in which the execution of elementary quantum algorithms is characterized by negligible errors. The proposed model has been entirely implemented in MATLAB, thus obtaining a software infrastructure for the analysis of Cr7Ni molecules that can be extended to quantum systems with analogous Hamiltonian and behavior.
Abstract This practical guide presents methods for constructing noise models using the Qiskit Aer noise module within the IBM Q ecosystem. The objective is to simulate quantum circuits under realistic error conditions, enabling accurate emulation of noisy quantum processors. The guide demonstrates how to: Use the Qiskit Aer noise module to define custom noise models. Incorporate gate errors, readout errors, and decoherence effects into simulations. Apply noise channels (e.g., depolarizing, amplitude damping, phase damping). Attach noise models to quantum circuit simulations. Analyze how noise affects algorithm performance and output distributions. Building noise models is essential for studying the behavior of quantum algorithms in the NISQ (Noisy Intermediate-Scale Quantum) era. It allows researchers to evaluate algorithm robustness, optimize circuit depth, and test error mitigation strategies before execution on real IBM Quantum hardware. This approach provides a bridge between ideal theoretical circuits and physically realistic quantum devices, enhancing the reliability and applicability of quantum computing experiments.