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Over the last few decades, quantum chemistry has progressed through the development of computational methods based on modern digital computers. However, these methods can hardly fulfill the exponentially-growing resource requirements when applied to large quantum systems. As pointed out by Feynman, this restriction is intrinsic to all computational models based on classical physics. Recently, the rapid advancement of trapped-ion technologies has opened new possibilities for quantum control and quantum simulations. Here, we present an efficient toolkit that exploits both the internal and motional degrees of freedom of trapped ions for solving problems in quantum chemistry, including molecular electronic structure, molecular dynamics, and vibronic coupling. We focus on applications that go beyond the capacity of classical computers, but may be realizable on state-of-the-art trapped-ion systems. These results allow us to envision a new paradigm of quantum chemistry that shifts from the current transistor to a near-future trapped-ion-based technology.
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Trapped-ion quantum information processors store information in atomic ions maintained in position in free space via electric fields. Quantum logic is enacted via manipulation of the ions internal and shared motional quantum states using optical and microwave signals. While trapped ions show great promise for quantum-enhanced computation, sensing, and communication, materials research is needed to design traps that allow for improved performance by means of integration of system components, including optics and electronics for ion-qubit control, while minimizing the near-ubiquitous electric-field noise produced by trap-electrode surfaces. In this review, we consider the materials requirements for such integrated systems, with a focus on problems that hinder current progress toward practical quantum computation. We give suggestions for how materials scientists and trapped-ion technologists can work together to develop materials-based integration and noise-mitigation strategies to enable the next generation of trapped-ion quantum computers.
Trapped ions (TI) are a leading candidate for building Noisy Intermediate-Scale Quantum (NISQ) hardware. TI qubits have fundamental advantages over other technologies such as superconducting qubits, including high qubit quality, coherence and connectivity. However, current TI systems are small in size, with 5-20 qubits and typically use a single trap architecture which has fundamental scalability limitations. To progress towards the next major milestone of 50-100 qubits, a modular architecture termed the Quantum Charge Coupled Device (QCCD) has been proposed. In a QCCD-based TI device, small traps are connected through ion shuttling. While the basic hardware components for such devices have been demonstrated, building a 50-100 qubit system is challenging because of a wide range of design possibilities for trap sizing, communication topology and gate implementations and the need to match diverse application resource requirements. Towards realizing QCCD systems with 50-100 qubits, we perform an extensive architectural study evaluating the key design choices of trap sizing, communication topology and operation implementation methods. We built a design toolflow which takes a QCCD architectures parameters as input, along with a set of applications and realistic hardware performance models. Our toolflow maps the applications onto the target device and simulates their execution to compute metrics such as application run time, reliability and device noise rates. Using six applications and several hardware design points, we show that trap sizing and communication topology choices can impact application reliability by up to three orders of magnitude. Microarchitectural gate implementation choices influence reliability by another order of magnitude. From these studies, we provide concrete recommendations to tune these choices to achieve highly reliable and performant application executions.
Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report on the experimental implementation of such an algorithm to solve a quantum chemistry problem, using a digital quantum simulator based on trapped ions. Specifically, we implement the variational quantum eigensolver algorithm to calculate the molecular ground state energies of two simple molecules and experimentally demonstrate and compare different encoding methods using up to four qubits. Furthermore, we discuss the impact of measurement noise as well as mitigation strategies and indicate the potential for adaptive implementations focused on reaching chemical accuracy, which may serve as a cross-platform benchmark for multi-qubit quantum simulators.
We present a quantum chemistry benchmark for noisy intermediate-scale quantum computers that leverages the variational quantum eigensolver, active space reduction, a reduced unitary coupled cluster ansatz, and reduced density purification as error mitigation. We demonstrate this benchmark on the 20 qubit IBM Tokyo and 16 qubit Rigetti Aspen processors via the simulation of alkali metal hydrides (NaH, KH, RbH),with accuracy of the computed ground state energy serving as the primary benchmark metric. We further parameterize this benchmark suite on the trial circuit type, the level of symmetry reduction, and error mitigation strategies. Our results demonstrate the characteristically high noise level present in near-term superconducting hardware, but provide a relevant baseline for future improvement of the underlying hardware, and a means for comparison across near-term hardware types. We also demonstrate how to reduce the noise in post processing with specific error mitigation techniques. Particularly, the adaptation of McWeeny purification of noisy density matrices dramatically improves accuracy of quantum computations, which, along with adjustable active space, significantly extends the range of accessible molecular systems. We demonstrate that for specific benchmark settings, the accuracy metric can reach chemical accuracy when computing over the cloud on certain quantum computers.
Fault-tolerant quantum computation promises to solve outstanding problems in quantum chemistry within the next decade. Realizing this promise requires scalable tools that allow users to translate descriptions of electronic structure problems to optimized quantum gate sequences executed on physical hardware, without requiring specialized quantum computing knowledge. To this end, we present a quantum chemistry library, under the open-source MIT license, that implements and enables straightforward use of state-of-art quantum simulation algorithms. The library is implemented in Q#, a language designed to express quantum algorithms at scale, and interfaces with NWChem, a leading electronic structure package. We define a standardized schema for this interface, Broombridge, that describes second-quantized Hamiltonians, along with metadata required for effective quantum simulation, such as trial wavefunction ansatzes. This schema is generated for arbitrary molecules by NWChem, conveniently accessible, for instance, through Docker containers and a recently developed web interface EMSL Arrows. We illustrate use of the library with various examples, including ground- and excited-state calculations for LiH, H$_{10}$, and C$_{20}$ with an active-space simplification, and automatically obtain resource estimates for classically intractable examples.
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