Scalable Emulation of Sign-Problem−-Free Hamiltonians with Room Temperature p-bits

The growing field of quantum computing is based on the concept of a q-bit which is a delicate superposition of 0 and 1, requiring cryogenic temperatures for its physical realization along with challenging coherent coupling techniques for entangling them. By contrast, a probabilistic bit or a p-bit is a robust classical entity that fluctuates between 0 and 1, and can be implemented at room temperature using present-day technology. Here, we show that a probabilistic coprocessor built out of room temperature p-bits can be used to accelerate simulations of a special class of quantum many-body systems that are sign-problem$-$free or stoquastic, leveraging the well-known Suzuki-Trotter decomposition that maps a $d$-dimensional quantum many body Hamiltonian to a $d$+1-dimensional classical Hamiltonian. This mapping allows an efficient emulation of a quantum system by classical computers and is commonly used in software to perform Quantum Monte Carlo (QMC) algorithms. By contrast, we show that a compact, embedded MTJ-based coprocessor can serve as a highly efficient hardware-accelerator for such QMC algorithms providing several orders of magnitude improvement in speed compared to optimized CPU implementations. Using realistic device-level SPICE simulations we demonstrate that the correct quantum correlations can be obtained using a classical p-circuit built with existing technology and operating at room temperature. The proposed coprocessor can serve as a tool to study stoquastic quantum many-body systems, overcoming challenges associated with physical quantum annealers.Comment: Fixed minor typos and expanded Appendi

Machine Learning Quantum Systems with Magnetic p-bits

The slowing down of Moore's Law has led to a crisis as the computing workloads of Artificial Intelligence (AI) algorithms continue skyrocketing. There is an urgent need for scalable and energy-efficient hardware catering to the unique requirements of AI algorithms and applications. In this environment, probabilistic computing with p-bits emerged as a scalable, domain-specific, and energy-efficient computing paradigm, particularly useful for probabilistic applications and algorithms. In particular, spintronic devices such as stochastic magnetic tunnel junctions (sMTJ) show great promise in designing integrated p-computers. Here, we examine how a scalable probabilistic computer with such magnetic p-bits can be useful for an emerging field combining machine learning and quantum physics

Accelerated Quantum Monte Carlo with Probabilistic Computers

Quantum Monte Carlo (QMC) techniques are widely used in a variety of scientific problems and much work has been dedicated to developing optimized algorithms that can accelerate QMC on standard processors (CPU). With the advent of various special purpose devices and domain specific hardware, it has become increasingly important to establish clear benchmarks of what improvements these technologies offer compared to existing technologies. In this paper, we demonstrate 2 to 3 orders of magnitude acceleration of a standard QMC algorithm using a specially designed digital processor, and a further 2 to 3 orders of magnitude by mapping it to a clockless analog processor. Our demonstration provides a roadmap for 5 to 6 orders of magnitude acceleration for a transverse field Ising model (TFIM) and could possibly be extended to other QMC models as well. The clockless analog hardware can be viewed as the classical counterpart of the quantum annealer and provides performance within a factor of $<10$ of the latter. The convergence time for the clockless analog hardware scales with the number of qubits as $\sim N$, improving the $\sim N^2$ scaling for CPU implementations, but appears worse than that reported for quantum annealers by D-Wave

The Non-Equilibrium Green Function (NEGF) Method

The Non-Equilibrium Green Function (NEGF) method was established in the 1960's through the classic work of Schwinger, Kadanoff, Baym, Keldysh and others using many-body perturbation theory (MBPT) and the diagrammatic theory for non-equilibrium processes. Much of the literature is based on the original MBPT-based approach and this makes it inaccessible to those unfamiliar with advanced quantum statistical mechanics. We obtain the NEGF equations directly from a one-electron Schr\"odinger equation using relatively elementary arguments. These equations have been used to discuss many problems of great interest such as quantized conductance, (integer) quantum Hall effect, Anderson localization, resonant tunneling and spin transport without a systematic treatment of many-body effects. But it goes beyond purely coherent transport allowing us to include phase-breaking interactions (both momentum-relaxing and momentum-conserving as well as spin-conserving and spin-relaxing) within a self-consistent Born approximation. We believe that the scope and utility of the NEGF equations transcend the MBPT-based approach originally used to derive it. NEGF teaches us how to combine quantum dynamics with "contacts" much as Boltzmann taught us how to combine classical dynamics with "contacts", using the word contacts in a broad, figurative sense to denote all kinds of entropy-driven processes. We believe that this approach to "contact-ing" the Schr\"odinger equation should be of broad interest to anyone working on device physics or non-equilibrium statistical mechanics in general.Comment: To appear in Springer Handbook of Semiconductor Devices (2021

Emulating Quantum Interference with Generalized Ising Machines

The recent groundbreaking demonstration of quantum supremacy in the noisy intermediate scale quantum (NISQ) era has led to an intense activity in establishing finer boundaries between classical and quantum computing. In this paper, we use quantum Monte Carlo (QMC) techniques to formulate a systematic procedure for translating any sequence of $d$ quantum gates acting on $n$ q-bits into a Boltzmann machine (BM) having $n+g(d)$ classical spins or p-bits with two values "0" and "1", but with a complex energy function $E$. Using this procedure we emulate Shor's algorithm with up to $36$ q-bits using $90$ p-bits, on an ordinary laptop computer in less than a day, while a naive Schr\"{o}dinger implementation would require multiplying matrices with $\approx 10^{21}$ elements. Even larger problems should be accessible on dedicated Ising Machines. However, we also identify clear limitations of the probabilistic approach by introducing a quantitative metric $S_{\text{Total}}$ for its inefficiency relative to a quantum computer. For example, a straightforward probabilistic implementation of Shor's algorithm with $n$ q-bits leads to an $S_{\text{Total}} \sim \exp{(-n/2)}$, making the computation time for the probabilistic Shor's algorithm scale exponentially as $2^{n/2}$ instead of the polynomial scaling expected for true quantum computers. This is a manifestation of the well-known sign problem in QMC and it may be possible to "tame" it with appropriate transformations. Finally, we present an example featuring a standard optimization algorithm based on a purely real energy function to which we add an imaginary part $\Im{(E)}$, thereby augmenting the statistical suppression of Feynman paths with quantum-like phase cancellation. This example illustrates how the sign problem encountered in classical annealers can potentially be turned into a computational resource for quantum annealers

Performance analysis of high efficiency InxGa1−xN/GaN intermediate band quantum dot solar cells

In this subsistent fifth generation era, InxGa1−xN/GaN based materials have played an imperious role and become promising contestant in the modernistic fabrication technology because of some of their noteworthy attributes. On our way of illustrating the performance, the structure of InxGa1−xN/GaN quantum dot (QD) intermediate band solar cell (IBSC) is investigated by solving the Schrödinger equation in light of the Kronig-Penney model. In comparison with p-n homojunction and heterojunction solar cells, InxGa1−xN/GaN IBQD solar cell manifests larger power conversion efficiency (PCE). PCE strongly depends on position and width of the intermediate bands (IB). Position of IBs can be controlled by tuning the size of QDs and the Indium content of InxGa1−xN whereas, width of IB can be controlled by tuning the interdot distance. PCE can also be controlled by tuning the position of fermi energy bands as well as changing the doping concentration. In this work, maximum conversion efficiency is found approximately 63.2% for a certain QD size, interdot distance, Indium content and doping concentration. Keywords: Solar cell, InxGa1−xN/GaN, Quantum dots, Intermediate band(s), Power conversion efficienc

Disease characteristics and serological responses in patients with differing severity of COVID-19 infection: A longitudinal cohort study in Dhaka, Bangladesh.

BackgroundCOVID-19 caused by SARS-CoV-2 ranges from asymptomatic to severe disease and can cause fatal and devastating outcome in many cases. In this study, we have compared the clinical, biochemical and immunological parameters across the different disease spectrum of COVID-19 in Bangladeshi patients.Methodology/principal findingsThis longitudinal study was conducted in two COVID-19 hospitals and also around the community in Dhaka city in Bangladesh between November 2020 to March 2021. A total of 100 patients with COVID-19 infection were enrolled and classified into asymptomatic, mild, moderate and severe cases (n = 25/group). In addition, thirty age and sex matched healthy participants were enrolled and 21 were analyzed as controls based on exclusion criteria. After enrollment (study day1), follow-up visits were conducted on day 7, 14 and 28 for the cases. Older age, male gender and co-morbid conditions were the risk factors for severe COVID-19 disease. Those with moderate and severe cases of infection had low lymphocyte counts, high neutrophil counts along with a higher neutrophil-lymphocyte ratio (NLR) at enrollment; this decreased to normal range within 42 days after the onset of symptom. At enrollment, D-dimer, CRP and ferritin levels were elevated among moderate and severe cases. The mild, moderate, and severe cases were seropositive for IgG antibody by day 14 after enrollment. Moderate and severe cases showed significantly higher IgM and IgG levels of antibodies to SARS-CoV-2 compared to mild and asymptomatic cases.Conclusion/significanceWe report on the clinical, biochemical, and hematological parameters associated with the different severity of COVID-19 infection. We also show different profile of antibody response against SARS-CoV-2 in relation to disease severity, especially in those with moderate and severe disease manifestations compared to the mild and asymptomatic infection