As proposed, we upgraded the system console on an existing Bruker Instruments, 14 T nuclear magnetic resonance (NMR) spectrometer to enable an improved implementation of type II quantum computers (TTQC). This upgrade is fully functional and has permitted our NMR studies to be moved to higher strength magnetic fields for better sensitivity and spectral dispersion. The TTQC experiments continue in collaboration with Dr. J. Yepez of the Air Force Research Laboratory. We have completed studies of the I-D dynamics of the diffusion equation and the Burger's equation with various viscosity. We have nearly completed additional studies showing both the scaling of errors in TTQC and a new novel mapping to reciprocal space lattices. The latter is hoped to be a first step toward running the TTQC with a closed feedback loop. The closed loop computations will permit continuous quantum computation in a lattice gas architecture.
As proposed, we upgraded the system console on an existing Bruker Instruments, 14 T nuclear magnetic resonance (NMR) spectrometer to enable an improved implementation of type II quantum computers (TTQC). This upgrade is fully functional and has permitted our NMR studies to be moved to higher strength magnetic fields for better sensitivity and spectral dispersion. The TTQC experiments continue in collaboration with Dr. J. Yepez of the Air Force Research Laboratory. We have completed studies of the I-D dynamics of the diffusion equation and the Burger's equation with various viscosity. We have nearly completed additional studies showing both the scaling of errors in TTQC and a new novel mapping to reciprocal space lattices. The latter is hoped to be a first step toward running the TTQC with a closed feedback loop. The closed loop computations will permit continuous quantum computation in a lattice gas architecture.
Recent work has demonstrated the feasibility of using an array of quantum information processors connected via classical channels (Type II Quantum Computer) to calculate the quantum lattice-gas algorithm. This thesis describes the construction and implementation of a new hardware scheme for a Type II Quantum computer. This system has different hardware and software specifications but does follow previously published approaches of operation encoding the initial mass density onto a two-qubit processor and using standard pulse techniques to step through the algorithm. New hardware for this system includes the use of multiple coils controlled by a hardware switch array as well as a full function, two channel spectrometer for dual readouts. New software includes a top-level control system for the spectrometer for quick experimental configuration as well as reconfigurable modeling software to verify results. Results are presented here for the quantum lattice gas algorithm for the diffusion equation run on two systems: a prototype configuration using a single coil in a 1.5 Tesla magnet and a final configuration using a coil array in a 5.0 Tesla magnet.*
*This dissertation is a compound document (contains both a paper copy and a CD as part of the dissertation). The CD requires the following system requirements: Adobe Acrobat.
Nuclear Magnetic Ressonance (NMR) is a widely used technique, with a long history of applications in chemestry, medicine, and material science. Twenty years ago, it emerged as a reliable source for quantum computing too, since the work of Cory. One of its major advantage is the ease with which arbitrary unitary transformations can be implemented, together with its experimental simplicity, that can be traced back to very simple NMR routines, which were being extensively used long before. However, some disadvantages came along, mostly related to experimental effort in the initialisation and measure processes, and scalability. In this work, we have successfully probed some simple quantum gates (Pauli-Z, Pauli-X and Hadamard) in one and two-qubit systems, realised in a NMR experiment. The work comprised a pseudo-pure state preparation, followed by the application of the gates, and a quantum tomography method, necessary to reconstruct the density matrix. The experiments were conducted with a chloroform sample, placed in a 300 MHz Bruker Avance II spectrometer, equipped with a superconducting magnet with a 7 T magnetic field.
Nuclear magnetic resonance offers an appealing prospect for implementation of quantum computers, because of the long coherence times associated with nuclear spins, and extensive laboratory experience in manipulating the spins with radio frequency pulses. Existing proposals, however, suffer from a signal-to-noise ratio that decays exponentially in the number of qubits in the quantum computer. This places a severe limit on the size of the computations that can be performed by such a computer; estimates of that limit are well within the range in which a conventional computer taking exponentially more steps would still be practical. We give an NMR implementation in which the signal-to-noise ratio depends only on features of NMR technology, not the size of the computer. This provides a means for NMR computation techniques to scale to sizes at which the exponential speedup enables quantum computation to solve problems beyond the capabilities of classical computers.
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.
There are two important related research areas that I propose to investigate. First, we plan to develop an efficient numerical integrator based on Fer expansion for solid-state NMR simulation of experiments. Second, we intend to extend the method to solve quantum Liouville equation and quantum Fokker-Planck equation in order to improve the understanding of the dynamics of quantum systems subject to dissipation due to its relation to macroscopic quantum phenomena. The goal of the proposed research is to study a numerical integrator based on Fer expansion (Fer integrators of higher orders) in the integration of the time-dependent Schrodinger equation (TDSE) which is a central problem to nuclear magnetic resonance in general and solid-state NMR (SSNMR) in particular. The Fer integrator will provide to experts in quantum mechanics, NMR spectroscopy, and spin dynamics researchers, additional means for controlling spin dynamics in SSNMR. The efficient diagram will be used to compare the different orders of the Fer integrators obtained.