Gate-controllable spin-orbit coupling is often one requisite for spintronic devices. For practical spin field-effect transistors, another essential requirement is ballistic spin transport, where the spin precession length is shorter than the mean free path such that the gate-controlled spin precession is not randomized by disorder. In this letter, we report the observation of a gate-induced crossover from weak localization to weak anti-localization in the magneto-resistance of a high-mobility two-dimensional hole gas in a strained germanium quantum well. From the magneto-resistance, we extract the phase-coherence time, spin-orbit precession time, spin-orbit energy splitting, and cubic Rashba coefficient over a wide density range. The mobility and the mean free path increase with increasing hole density, while the spin precession length decreases due to increasingly stronger spin-orbit coupling. As the density becomes larger than ∼6 × 1011 cm-2, the spin precession length becomes shorter than the mean free path, and the system enters the ballistic spin transport regime. We also report here the numerical methods and code developed for calculating the magneto-resistance in the ballistic regime, where the commonly used HLN and ILP models for analyzing weak localization and anti-localization are not valid. These results pave the way toward silicon-compatible spintronic devices.
This the final report of the LDRD project entitled "Realizing the Power of Near-Term Quantum Technologies", which was tasked with laying a theoretical foundation and computational framework for quantum simulation on quantum devices, to support both future Sandia efforts and the broader academic research effort in this area. The unifying theme of the project has been the desire to delineate more clearly the interface between existent classical computing resources that are vast and reliable with emerging quantum computing resources that will be scarce and unreliable for the foreseeable future. We seek to utilize classical computing resources to judge the efficacy of quantum devices for quantum simulation tasks and determine when they exceed the performance of classical devices, thereby achieving "quantum supremacy". This task was initially pursued by adapting the general concept of "parameter space compression" to quantum simulation. An inability to scale this analysis efficiently to large-scale simulations precipitated a shift in focus to assessing quantum supremacy of a specific quantum device, a 1D Bose gas trapped in an optical lattice, that was more amenable to large-scale analysis. We also seek to reconstruct unobserved information from limited observations of a quantum device to enhance their utility. This task was initially pursued as an application of maximum entropy reconstruction. Initial attempts to improve entropy approximations for direct reconstruction by free energy minimization proved to be more difficult than expected, and the focus shifted to the development of a quantum thermostat to facilitate indirect reconstruction by evolving a quantum Markov process. An efficient quantum thermostat is broadly useful for quantum state preparation in almost any quantum simulation task. In the middle of the project, a small opportunistic investment was made in a high-risk experiment to build an analog quantum simulator out of hole quantum dots in Ge/SiGe heterostructures. While a useful simulator was not produced, hole quantum dots at a Ge/SiGe interface have been successfully observed for the first time.
This paper describes our work over the past few years to use tools from quantum chemistry to describe electronic structure of nanoelectronic devices. These devices, dubbed "artificial atoms", comprise a few electrons, con ned by semiconductor heterostructures, impurities, and patterned electrodes, and are of intense interest due to potential applications in quantum information processing, quantum sensing, and extreme-scale classical logic. We detail two approaches we have employed: nite-element and Gaussian basis sets, exploring the interesting complications that arise when techniques that were intended to apply to atomic systems are instead used for artificial, solid-state devices.
Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(-1)) poles to achieve an error tolerance at temperature β-1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δocc, the occupied energy interval. This is particularly beneficial when Δ ≫ Δocc, such as in electronic structure calculations that use a large basis set.
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and correct errors, while color codes have transversal Clifford gates and better code efficiency in the number of physical qubits needed to achieve a given code distance. A formal equivalence exists between color codes and folded surface codes, but it does not guarantee the transferability of any of these favorable properties. However, the equivalence does imply the existence of constant-depth circuit implementations of logical Clifford gates on folded surface codes. We achieve and improve this result by constructing two families of folded surface codes with transversal Clifford gates. This construction is presented generally for qudits of any dimension. The specific application of these codes to universal quantum computation based on qubit fusion is also discussed.
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and correct errors, while color codes have transversal Clifford gates and better code efficiency in the number of physical qubits needed to achieve a given code distance. A formal equivalence exists between color codes and folded surface codes, but it does not guarantee the transferability of any of these favorable properties. However, the equivalence does imply the existence of constant-depth circuit implementations of logical Clifford gates on folded surface codes. We achieve and improve this result by constructing two families of folded surface codes with transversal Clifford gates. This construction is presented generally for qudits of any dimension. Lastly, the specific application of these codes to universal quantum computation based on qubit fusion is also discussed.
We consider four-dimensional qudits as qubit pairs and their qudit Pauli operators as qubit Clifford operators. This introduces a nesting, C21 ⊂ C42 ⊂ C23, where Cmn is the nth level of the m-dimensional qudit Clifford hierarchy. If we can convert between logical qubits and qudits, then qudit Clifford operators are qubit non-Clifford operators. Conversion is achieved by qubit fusion and qudit fission using stabilizer circuits that consume a resource state. This resource is a fused qubit stabilizer state with a fault- tolerant state preparation using stabilizer circuits.
We lay the foundation for a benchmarking methodology for assessing current and future quantum computers. We pose and begin addressing fundamental questions about how to fairly compare computational devices at vastly different stages of technological maturity. We critically evaluate and offer our own contributions to current quantum benchmarking efforts, in particular those involving adiabatic quantum computation and the Adiabatic Quantum Optimizers produced by D-Wave Systems, Inc. We find that the performance of D-Wave's Adiabatic Quantum Optimizers scales roughly on par with classical approaches for some hard combinatorial optimization problems; however, architectural limitations of D-Wave devices present a significant hurdle in evaluating real-world applications. In addition to identifying and isolating such limitations, we develop algorithmic tools for circumventing these limitations on future D-Wave devices, assuming they continue to grow and mature at an exponential rate for the next several years.