Héctor J. García

Simulation of Quantum Circuits via Stabilizer Frames

Generic quantum-circuit simulation appears intractable for conventional computers and may be unnecessary because useful quantum circuits exhibit significant structure that can be exploited during simulation. For example, Gottesman and Knill identified an important subclass, called stabilizer circuits, which can be simulated efficiently using group-theory techniques and insights from quantum physics. Realistic circuits enriched with quantum error-correcting codes and fault-tolerant procedures are dominated by stabilizer subcircuits and contain a relatively small number of non-Clifford components. Therefore, we develop new data structures and algorithms that facilitate parallel simulation of such circuits. Stabilizer frames offer more compact storage than previous approaches but require more sophisticated bookkeeping. Our implementation, called Quipu, simulates certain quantum arithmetic circuits (e.g., reversible ripple-carry adders) in polynomial time and space for equal superpositions of n-qubits. On such instances, known linear-algebraic simulation techniques, such as the (state-of-the-art) BDD-based simulator QuIDDPro, take exponential time. We simulate quantum Fourier transform and quantum fault-tolerant circuits using Quipu, and the results demonstrate that our stabilizer-based technique empirically outperforms QuIDDPro in all cases. While previous high-performance, structure-aware simulations of quantum circuits were difficult to parallellize, we demonstrate that Quipu can be parallelized with a nontrivial computational speedup.

Quipu: High-performance simulation of quantum circuits using stabilizer frames

As quantum information processing gains traction, its simulation becomes increasingly significant for engineering purposes - evaluation, testing and optimization - as well as for theoretical research. Generic quantum-circuit simulation appears intractable for conventional computers. However, Gottesman and Knill identified an important subclass, called stabilizer circuits, which can be simulated efficiently using group-theory techniques. Practical circuits enriched with quantum error-correcting codes and fault-tolerant procedures are dominated by stabilizer subcircuits and contain a relatively small number of non-stabilizer components. Therefore, we develop new group-theory data structures and algorithms to simulate such circuits. Stabilizer frames offer more compact storage than previous approaches but requires more sophisticated bookkeeping. Our implementation, called Quipu, simulates certain quantum arithmetic circuits (e.g., ripple-carry adders) in polynomial time and space for equal superpositions of n-qubits. On such instances, known linear-algebraic simulation techniques, such as the (state-of-the-art) BDD-based simulator QuIDDPro, take exponential time. We simulate various quantum Fourier transform and quantum fault-tolerant circuits with Quipu, and the results demonstrate that our stabilizer-based technique outperforms QuIDDPro in all cases.

Abstract 4925: The natural enzyme sequestration in signaling cascades provides inherent opportunities for off-target effects induced by kinase inhibitors

Proceedings: AACR 103rd Annual Meeting 2012‐‐ Mar 31‐Apr 4, 2012; Chicago, IL Off-target effects from targeted therapies are often attributed to cross-talk, which usually refers to inter-pathway molecular interactions that occur because of explicit regulatory feedback connections between two pathways. Recent experimental and theoretical studies have demonstrated, however, that covalently modified cascades naturally exhibit bidirectional signal propagation via a phenomenon termed retroactivity. This phenomenon arises due to enzyme sequestration where each cycle is coupled, not only to the next cycle, but also to the previous cycle. While retroactivity occurs naturally in covalently modified cascades, signaling pathways likely evolved to propagate information in a downstream manner. An important consequence of retroactivity, however, is that a downstream perturbation can induce an upstream response without the presence of regulatory feedback connections. We hypothesize that kinase inhibitors can produce off-target effects as a consequence of retroactivity alone via the following mechanism: a signal travels upstream from the site of a downstream perturbation through retroactivity and, upon reaching a shared upstream component, is delivered to an independent parallel pathway. To test the hypothesis we used a computational model to simulate the targeted inhibition of a specific kinase in a series signaling networks using physiologically and therapeutically relevant ranges for all parameters. Surprisingly, our results suggest that an off-target effect due to retroactive signaling is more likely when the first cycle in a non-inhibited cascade is “off” and not consuming large amounts of a shared up-stream activator. Our results also suggest that the kinetics governing covalently modified cycles in a cascade are more important for propagating an upstream off-target effect than the binding affinity of the drug to the targeted protein, which is a commonly optimized property in drug development. Finally, our results suggest that a single mutation has the capacity to produce a large spontaneous off-target effect without any direct regulatory connections between the targeted protein and the effected protein. Together, our results suggest that retroactivity may play an important role in the dysregulated signaling networks of cancer cells as well as the cellular response to targeted therapies. These findings have important implications for somatic evolution in cancer and the onset of therapeutic resistance, which has been widely reported for many targeted cancer therapeutics, including kinase inhibitors. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 103rd Annual Meeting of the American Association for Cancer Research; 2012 Mar 31-Apr 4; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2012;72(8 Suppl):Abstract nr 4925. doi:1538-7445.AM2012-4925

Abstract 4907: Elucidating the role of retroactive signaling and kinase inhibitors on off-target drug effects

The primary objective of targeted cancer therapies is to modulate cancer progression by perturbing specific molecules involved in aberrant proliferation and invasion. Kinase inhibitors are targeted therapies which are designed to interfere with a specific kinase molecule in a dysregulated oncogenic signaling cascade. While extremely promising as anti-cancer agents, such inhibitors may have undesirable off-target effects, whether by non-specific interactions or by effects from pathway cross-talk. We have shown in published experimental and theoretical work that covalently modified signaling cascades naturally exhibit bidirectional signal propagation. This phenomenon is termed retroactivity and challenges the widespread notion that information in cascades only flows from the cell surface to the nucleus. Previous work has demonstrated that increasing the concentration of a phosphatase in the terminal cycle of a covalently modified cascade may result in a measurable decrease in the concentration of the previous cycle9s activated kinase. Thus, a downstream perturbation in a signaling cascade can produce a reverse (or retroactive) response without the need for direct negative feedback connections. This led us to hypothesize that the use of an inhibitory drug in a signaling network may cause an upstream off-target effect simply by inhibiting the activation or deactivation of a downstream kinase. To test the hypothesis that retroactivity contributes to off-target effects, we extended our previous work to a computational model that tested a series of signaling networks. The objective of our approach was two-fold: (1) to probe the effect of retroactivity on a kinase inhibitor in a signaling network and (2) to test whether retroactivity is likely to produce a measurable off-target effect under physiologically realistic conditions. Specifically, our model simulates the targeted inhibition of an activated kinase in a series of multi-cycle networks. The results of our work indicate that at physiologically and therapeutically relevant concentrations, a targeted inhibitor may induce a measurable off-target effect via retroactivity. We also performed local sensitivity analyses to predict the kinetic parameters that most affect the off-target response. Surprisingly, the drug disassociation constant is predicted to have very little effect while parameters such as the enzyme saturation and maximum velocity of some cycles are predicted to be very important. A proper characterization of a pathway9s structure is important for identifying which protein in the pathway represents the optimal drug target as well as what concentration of the targeted therapy is likely to modulate the pathway in the manner desired. We believe our results support the position that such characterizations should consider the role of retroactivity as a source of a potential off-target effects by kinase inhibitors. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 102nd Annual Meeting of the American Association for Cancer Research; 2011 Apr 2-6; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2011;71(8 Suppl):Abstract nr 4907. doi:10.1158/1538-7445.AM2011-4907

Spinto: high-performance energy minimization in spin glasses

With the prospect of atomic-scale computing, we study cumulative energy profiles of spin-spin interactions in non-ferromagnetic lattices (Ising spin-glasses)-an established topic in solid-state physics that is now becoming relevant to atomic-scale EDA. Recent proposals suggest non-traditional computing devices based on natures ability to find min-energy states. Spinto utilizes EDA-inspired high-performance algorithms to (i) simulate natural energy minimization in spin systems and (ii) study its potential for solving hard computational problems. Unlike previous work, our algorithms are not limited to planar Ising topologies. In one CPU-day, our branch-and-bound algorithm finds min-energy (ground) states on 100 spins, while our local search approximates ground states on 1,000,000 spins. We use this computational tool to study the significance of hyper-couplings in the context of recently implemented adiabatic quantum computers.

Abstract 3174: Visualization of the activation/deactivation cycle of RhoC in inflammatory breast cancer

Proceedings: AACR 101st Annual Meeting 2010‐‐ Apr 17‐21, 2010; Washington, DC A key event in the development of Inflammatory Breast Cancer, a particularly aggressive, metastatic form of breast cancer, is the over-expression of the GTPase protein RhoC. RhoC plays a role in regulating cell shape, attachment and motility and over-expression is likely associated with tumor proliferation. RhoC is activated into a GTP-bound state by the regulatory proteins GEFs (guanine nucleotide exchange factor proteins) and is deactivated to a GDP-bound state by GAPs (GTPase activating proteins). Stimulation of IBC cells with LPA (lysophophatidic acid), an activator of the cycle, showed a transient RhoC-GTP increase, peaking at 2 minutes and then diminishing until 20 minutes. It has been suggested that LPA can activate both GEF and GAP proteins, and that a delay in the GAP protein activation could explain this RhoC-GTP behavior. Because RhoC activity occurs at the plasma membrane, the translocation of GEF and GAP proteins was studied as an indication of RhoC interaction. Immunofluorescent stains for the three key proteins\_RhoC, GAP, and GEF\_were performed on an IBC cell line before and after stimulation with LPA and observed using confocal microscopy. Preliminary images revealed a co-localization of three proteins RhoC, p190B (a GAP protein), and PDZ (a GEF protein) in the cytosol, forming a gradient of high to low protein concentration from the nuclear membrane to the plasma membrane. Further analysis with ImageJ software showed slight differences in protein concentration at the two membranes upon stimulation with LPA. RhoC protein levels increased at both membranes, PDZ quantities increased slightly at the plasma membrane, and the p190B levels decreased at both membranes as a result of stimulation. This data suggests that after 5 minutes, LPA has a positive regulatory effect on the GEF protein and a negative one on the GAP protein at the plasma membrane. In addition, co-localization of the proteins RhoC and p190B was analyzed at different time points. The data indicates a decrease in co-localization after LPA stimulation that is slightly recovered 20 minutes after treatment. A possible explanation for these results is that 5 minutes after stimulation, RhoC undergoes translocation to the nuclear and plasma membranes, and is not followed by the GAP protein until later times. As of now, these conclusions are preliminary. These results will be verified using a new RhoC antibody, and additional co-localization analysis. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 101st Annual Meeting of the American Association for Cancer Research; 2010 Apr 17-21; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2010;70(8 Suppl):Abstract nr 3174.

Abstract 2012: Off-target drug effects due to retroactivity in signaling pathways

A majority of targeted cancer therapeutics involve the specific inhibition of a molecular target in a signal transduction pathway. It is well known that targeted therapies, such as kinase inhibitors, may have effects on pathways other than those specifically targeted, whether by non-specific interactions or by indirect pathway cross-talk effects. The simplest view of signal transduction entails a cascade of molecular events initiated by the recognition of a stimulus and culminating in the chemical alteration of an effector molecule. We have recently shown that cascades can exhibit bidirectional signal propagation without the addition of regulatory feedback connections via a phenomenon termed retroactivity. Thus, retroactivity represents another potential source of off-target effects in signaling cascades. We have extended our previous work to a computational model which allows us to characterize the significance of the upstream off-target effect via retroactivity with a series of simple signaling networks using physiologically relevant parameters values. We aim to understand the dynamics of cancer signaling by integrating systems biology based models of signaling dynamics into our experimental investigations of breast cancer with the intent of both directing experiments and making predictions. One of the signaling networks we studied takes the form of two independent signaling cascades which have no regulatory feedback connections but are activated by the same upstream kinase. Our results suggest that under physiologically relevant conditions the application of an inhibitor near the bottom of one cascade can produce a significant change in concentration of a protein in the other cascade, even without a regulatory feedback connection between the two cascades. Developing a deeper understanding of bidirectional signal propagation in signal transduction pathways will be vitally important in the effort to develop safer and more effective targeted cancer therapies. Our modeling results challenge the notion that information in cascades only flows in the cell surface-to-nucleus direction and suggests that a perturbation applied within a cascade can produce both an upstream and a downstream effect. The notion of an upstream off-target effect is completely novel and may have significant implications if the perturbation takes the form of an inhibitory therapeutic drug. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 101st Annual Meeting of the American Association for Cancer Research; 2010 Apr 17-21; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2010;70(8 Suppl):Abstract nr 2012.