With the surge of quantum computing platforms that continue to push the boundaries of capabilities of noisy intermediate-scale quantum computers, there is a growing interest in finding relevant applications and quantifying the corresponding error budgets. We present a simulation of nuclear magnetic resonance (NMR) spectroscopy of small organic molecules on publicly available cloud quantum computers. We are using two quantum computing platforms, namely IBM's quantum processors based on superconducting qubits and IonQ's Aria trapped ion quantum computer addressed via Amazon Braket. We analyze the impact of noise on the obtained NMR spectra, and we formulate an effective decoherence rate that quantifies the threshold noise that our proposed algorithm can tolerate. We show that the effective decoherence rate can be calculated using simple fidelity metrics that are available by cloud quantum computing providers. Our investigation paves the way to better employ such application-driven quantum tasks on current noisy quantum devices.
With the surge of quantum computing platforms that continue to push the boundaries of capabilities of noisy intermediate-scale quantum computers, there is a growing interest in finding relevant applications and quantifying the corresponding error budgets. We present a simulation of nuclear magnetic resonance (NMR) spectroscopy of small organic molecules on publicly available cloud quantum computers. We are using two quantum computing platforms, namely IBM's quantum processors based on superconducting qubits and IonQ's Aria trapped ion quantum computer addressed via Amazon Braket. We analyze the impact of noise on the obtained NMR spectra, and we formulate an effective decoherence rate that quantifies the threshold noise that our proposed algorithm can tolerate. We show that the effective decoherence rate can be calculated using simple fidelity metrics that are available by cloud quantum computing providers. Our investigation paves the way to better employ such application-driven quantum tasks on current noisy quantum devices.
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.
Simulating nuclear magnetic resonance (NMR) spectra is a promising application of quantum simulation. Using Quantinuum's System Model H2, a trapped-ion quantum computer, we demonstrate an end-to-end, large-scale digital NMR simulation of a classically challenging benchmark molecule, 1,2-di-tert-butyl-diphosphane. We implement a hardware-efficient reduction of the nuclear-spin Hamiltonian, enabling Trotterized real-time evolution of an effective 21-spin model with tailored error suppression to reduce the effects of device noise. The reconstructed liquid-state proton NMR spectrum agrees with classical reference calculations and reproduces key spectroscopic features that previous quantum hardware demonstrations did not capture. Given the widespread use of NMR in chemical analysis and industrial research, these results advance digital quantum simulation of NMR spectra towards practical quantum utility.
While the recent demonstration of accurate computations of classically intractable simulations on noisy quantum processors brings quantum advantage closer, there is still the challenge of demonstrating it for practical problems. Here we investigate the application of noisy intermediate-scale quantum devices for simulating nuclear magnetic resonance (NMR) experiments in the high-field regime. In this work, the NMR interactions are mapped to a quantum device via a product formula with minimal resource overhead, an approach that we discuss in detail. Using this approach, we show the results of simulations of liquid-state proton NMR spectra on relevant molecules with up to 11 spins, and up to a total of 47 atoms, and compare them with real NMR experiments. Despite current limitations, we show that a similar approach will eventually lead to a case of quantum utility, a scenario where a practically relevant computational problem can be solved by a quantum computer but not by conventional means. We provide an experimental estimation of the amount of quantum resources needed for solving larger instances of the problem with the presented approach. The polynomial scaling we demonstrate on real processors is a foundational step in bringing practical quantum computation closer to reality.
Quantum computing is at the cusp of showing relevance for real-world problems. However, currently available devices are small in scale, and hardware demonstrations have shown limited applicability to scientific and commercial problems of interest. In this work, we investigate a set of application-specific noisy intermediate-scale quantum (NISQ) algorithms varying in size from 4-80 qubits, and use these benchmarks to evaluate trade-offs in the design of trapped ion quantum computing architectures. We have developed a tool-chain consisting of architecture specific compilation and simulation tools and used these tools to target five different candidate trapped ion quantum computing architectures. Using our tool-chain, we can estimate metrics such as application run-times and overhead. Additionally, we use our tools to determine the critical operations of an architecture and to study the sensitivity to architectural constraints in particular implementations. Our tools are designed to be flexible, allowing us to study a broad range of benchmarks, hardware architectures, physical constraints, and operation timing.
Quantum devices in the noisy intermediate-scale quantum (NISQ) era are highly susceptible to different types of quantum noise, which directly impact the reliability of experimental results. This work provides a characterization of error behavior arising from quantum noises on IBM's superconducting quantum processor, offering practical insights for algorithm design, benchmarking, and error-mitigation strategies on a real superconducting quantum processor in the NISQ era. The study begins with the measurement of the basis state, without applying any gate, to quantify state-preparation and measurement (SPAM) errors. Additionally, the errors are further quantified due to the application of single-qubit Pauli-X, two-qubit CNOT gate and other multi-qubit Controlled-X gates. Each circuit was executed with 1024 shots, and the percentage error between the expected and observed outputs was computed. The results show that the single-qubit Pauli-X gate exhibits relatively low errors in comparison with the two-qubit CNOT gate, whereas other multi-qubit Controlled-X gates lead to significantly higher deviations. This work also analyzes the noise effect of a fourqubit Controlled-X gate being implemented using a three-qubit Controlled-X gate with an extra auxiliary qubit, and the result shows a significant reduction in the error rate.
Simulations of nuclear magnetic resonance (NMR) experiments can be an important tool for extracting information about molecular structure and optimizing experimental protocols but are often intractable on classical computers for large molecules such as proteins and for protocols such as zero-field NMR. We demonstrate the first quantum simulation of an NMR spectrum, computing the zero-field spectrum of the methyl group of acetonitrile using four qubits of a trapped-ion quantum computer. We reduce the sampling cost of the quantum simulation by an order of magnitude using compressed sensing techniques. We show how the intrinsic decoherence of NMR systems may enable the zero-field simulation of classically hard molecules on relatively near-term quantum hardware and discuss how the experimentally demonstrated quantum algorithm can be used to efficiently simulate scientifically and technologically relevant solid-state NMR experiments on more mature devices. Our work opens a practical application for quantum computation.