We experimentally compute relativistic and correlation effects in the atomic properties by using a superconducting qubit processor. Specifically, we compute the relativistic ground-state energies and magnetic-dipole hyperfine structure constants for four Li-like atomic systems ranging from very light to moderately heavy to very heavy in terms of nuclear charge. A symmetry-conserving Bravyi-Kitaev transformation is used to reduce the original six-qubit problem to a four-qubit problem, which is experimentally contrived by reducing the hardware requirement by employing a virtual two-qubit gate. It enables the simulation of four-qubit circuits using two physical qubits with additional circuit evaluations. The ground-state wave functions, required for computing atomic properties, are obtained by using quantum state tomography. Our results show that the averaged relative errors for the ground-state energies are ≈ 0.3 ± 1 % . However, for the hyperfine structure constants, the mean values of the relative errors are less than 15 % , with their estimated upper bound of relative errors of ≈ ± 10 % (with the exception of 7.2 ± 47 % for neutral Li 7 ). Notably, our results for the hyperfine structure constants exhibit higher sensitivity to errors as compared to energies; a trend which we also confirm through additional numerical simulations. Published by the American Physical Society 2024
We experimentally compute relativistic and correlation effects in the atomic properties by using a superconducting qubit processor. Specifically, we compute the relativistic ground-state energies and magnetic-dipole hyperfine structure constants for four Li-like atomic systems ranging from very light to moderately heavy to very heavy in terms of nuclear charge. A symmetry-conserving Bravyi-Kitaev transformation is used to reduce the original six-qubit problem to a four-qubit problem, which is experimentally contrived by reducing the hardware requirement by employing a virtual two-qubit gate. It enables the simulation of four-qubit circuits using two physical qubits with additional circuit evaluations. The ground-state wave functions, required for computing atomic properties, are obtained by using quantum state tomography. Our results show that the averaged relative errors for the ground-state energies are ≈ 0.3 ± 1 % . However, for the hyperfine structure constants, the mean values of the relative errors are less than 15 % , with their estimated upper bound of relative errors of ≈ ± 10 % (with the exception of 7.2 ± 47 % for neutral Li 7 ). Notably, our results for the hyperfine structure constants exhibit higher sensitivity to errors as compared to energies; a trend which we also confirm through additional numerical simulations. Published by the American Physical Society 2024
We report the first results of the magnetic dipole hyperfine structure (HFS) constants of neutral Li, Li-like Be, neutral Na, and Na-like Mg using a modified version of the Quantum Annealer Eigensolver (QAE) algorithm on D-Wave's quantum hardware. The results are benchmarked against relativistic configuration interaction with multiconfiguration Dirac Hartree-Fock (MCDHF) calculations using the General-purpose Relativistic Atomic Structure Package (GRASP), and simulated annealing. In our modified QAE, a zooming-and-sigma-annealing approach with a floating-point encoding scheme is adopted to estimate the ground-state eigenvalue and eigenvector of the relativistic Dirac-Coulomb Hamiltonian matrices (HDC) constructed from 11 or fewer configuration state functions (CSFs). For calculations with extended correlation orbital sets, we applied a CSF truncation scheme, retaining only CSFs (up to 12) that make significant contributions to the ground-state wavefunction. Our modified QAE precision is kept limited to three decimal places (up to 10 qubits). Hardware demonstrations on the D-Wave quantum processing unit (QPU) yielded results that were completely consistent with GRASP (at the chosen precision) in determining the magnetic dipole HFS constants, with accuracy varying across systems and HDC matrix dimensions.
Although near-term quantum computing devices are still limited by the quantity and quality of qubits in the so-called NISQ era, quantum computational advantage has been experimentally demonstrated. Moreover, hybrid architectures of quantum and classical computing have become the main paradigm for exhibiting NISQ applications, where low-depth quantum circuits are repeatedly applied. In order to further scale up the problem size solvable by the NISQ devices, it is also possible to reduce the number of physical qubits by "cutting" the quantum circuit into different pieces. In this work, we experimentally demonstrated a circuit-cutting method for simulating quantum circuits involving many logical qubits, using only a few physical superconducting qubits. By exploiting the symmetry of linear-cluster states, we can estimate the effectiveness of circuit-cutting for simulating up to 33-qubit linear-cluster states, using at most 4 physical qubits for each subcircuit. Specifically, for the 12-qubit linear-cluster state, we found that the experimental fidelity bound can reach as much as 0.734, which is about 19% higher than a direct implementation on the same 12-qubit superconducting processor. Our results indicate that circuit-cutting represents a feasible approach of simulating quantum circuits using much fewer qubits, while achieving a much higher circuit fidelity.
An important aspect that strongly impacts the experimental feasibility of quantum circuits is the ratio of gate times and typical error time scales. Algorithms with circuit depths that significantly exceed the error time scales will result in faulty quantum states and error correction is inevitable. We present a comparison of the theoretical minimal gate time, i.e., the quantum speed limit (QSL), for realistic two- and multi-qubit gate implementations in neutral atoms and superconducting qubits. Subsequent to finding the QSLs for individual gates by means of optimal control theory we use them to quantify the circuit QSL of the quantum Fourier transform and the quantum approximate optimization algorithm. In particular, we analyze these quantum algorithms in terms of circuit run times and gate counts both in the standard gate model and the parity mapping. We find that neutral atom and superconducting qubit platforms show comparable weighted circuit QSLs with respect to the system size. Published by the American Physical Society 2024
Quantum processors have the potential to significantly advance our understanding of quantum systems. In particular, the programmability of digital quantum devices enables access to highly tunable quantum dynamics and observables. The central challenge, however, is suppressing errors, making quantum error correction essential for large-scale algorithms. In this thesis, I present work on quantum processing with reconfigurable atom arrays, with experiments featuring up to 448 neutral atom qubits, high two-qubit gate fidelities, arbitrary connectivity, and mid-circuit qubit readout and reuse. Using this system, I describe how we realize gate-based quantum simulations. In particular, we experimentally study Kitaev’s honeycomb model and explore hardware-efficient fermion-to-qubit encodings. We then leverage unique opportunities with atoms to study the key building blocks of scalable quantum error correction. These include below-threshold performance, deep computation at constant entropy, and universal logical gates. Together, these experiments highlight unique near-term opportunities with atom arrays and chart a path toward future large-scale atomic processors.
Developing methods to solve nuclear many-body problems with quantum computers is an imperative pursuit within the nuclear physics community. Here, we introduce a quantum algorithm to accurately and precisely compute the ground state of valence two-neutron systems leveraging presently available noisy intermediate-scale quantum devices. Our focus lies on the nuclei having a doubly magic core plus two valence neutrons in the p,sd, and pf shells, i.e., 6He,18O, and 42Ca, respectively. Our ansatz, quantum circuit, is constructed in the pair-wise form, taking into account the symmetries of the system in an explicit manner, and enables us to reduce the number of qubits and the number of CNOT gates required. The results on a real quantum hardware by IBM Quantum Platform show that the proposed method gives very accurate results of the ground-state energies, which are typically within 0.1 error in the energy for 6He and 18O and at most 1 error for 42Ca. Furthermore, our experiments using real quantum devices also show the pivotal role of the circuit layout design, attuned to the connectivity of the qubits, in mitigating errors.
Quantum computing holds the promise of solving problems that are intractable for classical computers, with applications ranging from optimization and materials simulation to cryptography. It achieves this by leveraging the exponentially scaling dimensionality of the space encoding quantum information and by executing algorithms on quantum registers in superposition states – a feature often referred to as quantum parallelism. However, while encoding information in computational units capable of exploring a continuous set of quantum states enables exponential scaling of computational power with system size, quantum systems are also more susceptible to errors than their classical counterparts. These errors take the form of both control errors, where miscalibration of the control pulses causes coherent errors on the qubit states, as well as incoherent errors due to energy relaxation and dephasing. Scaling quantum systems to run useful algorithms involving hundreds or thousands of logical qubits will require quantum error correction. In this approach, quantum information is redundantly encoded across an entangled state of many physical qubits. This has enabled experimental demonstrations across various platforms – including ion traps, superconducting circuits, and neutral atoms – showing that encoded quantum states can be preserved beyond the coherence times of the constituting physical qubits. However, quantum state preservation is only one component needed for scalable quantum computing. To execute algorithms, it is also necessary to implement quantum gates on and between encoded qubits, in a way that maintains fault tolerance by preserving the ability to correct errors as they occur during the computation. In the first part of this thesis, we demonstrate the implementation of an error-corrected quantum operation that entangles two logical qubits. This is achieved by performing lattice surgery on a distance-three surface code qubit, resulting in a logical Bell state encoded in distance-three repetition codes, which enable the correction of single bit-flip errors. We further introduce techniques to benchmark and characterize the performance of logical operations, including applying the protocol to arbitrary logical input states and performing logical quantum process tomography. Together, these results constitute one of the first realizations of error-corrected lattice surgery in superconducting circuits. While quantum error correction can correct errors provided they occur with sufficiently low frequency, it may fail when many qubits experience errors simultaneously. In the second part of this thesis, we therefore shift focus to a specific error mechanism known to cause correlated errors in superconducting circuits – quasiparticle-induced decoherence. In this case, various forms of energy deposition on the quantum device can break Cooper pairs into quasiparticles, which may subsequently diffuse to the tunnel junction and interact with the qubit state, thereby causing decoherence. In this thesis, we investigate the impact of quasiparticle tunneling on qubit performance, with a focus on infrared-induced quasiparticles. We compare the sensitivity of niobium-based qubits to those made from tantalum – a material that has gained interest in recent years following demonstrations of qubits with improved coherence times based on this material. Using a thermal radiator source, we show that the performance of tantalum qubits may be limited by infrared-induced quasiparticles in typical superconducting circuit experimental setups. By employing both ambient and in-line infrared filters, we investigate the effectiveness of different filtering strategies and develop best practices for engineering cryogenic environments for superconducting quantum processors. The results presented in this thesis contribute to the advancement of quantum computing based on superconducting circuits by implementing and characterizing quantum error-corrected operations, and by investigating quasiparticles as a source of decoherence, along with strategies to improve infrared filtering and signal conditioning in cryogenic environments for future fault-tolerant quantum computing.