1,478 research outputs found
Scalable Emulation of Sign-ProblemFree 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-problemfree or stoquastic, leveraging the well-known
Suzuki-Trotter decomposition that maps a -dimensional quantum many body
Hamiltonian to a +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
Matching Preclusion and Conditional Matching Preclusion Problems for Twisted Cubes
The matching preclusion number of a graph is the minimum
number of edges whose deletion results in a graph that has neither
perfect matchings nor almost-perfect matchings. For many interconnection
networks, the optimal sets are precisely those induced by a
single vertex. Recently, the conditional matching preclusion number
of a graph was introduced to look for obstruction sets beyond those
induced by a single vertex. It is defined to be the minimum number
of edges whose deletion results in a graph with no isolated vertices
that has neither perfect matchings nor almost-perfect matchings. In
this paper, we find the matching preclusion number and the conditional matching preclusion number for twisted cubes, an improved
version of the well-known hypercube. Moreover, we also classify all
the optimal matching preclusion sets
On the Method of Interconnection and Damping Assignment Passivity-Based Control for the Stabilization of Mechanical Systems
Interconnection and damping assignment passivity-based control (IDA-PBC) is
an excellent method to stabilize mechanical systems in the Hamiltonian
formalism. In this paper, several improvements are made on the IDA-PBC method.
The skew-symmetric interconnection submatrix in the conventional form of
IDA-PBC is shown to have some redundancy for systems with the number of degrees
of freedom greater than two, containing unnecessary components that do not
contribute to the dynamics. To completely remove this redundancy, the use of
quadratic gyroscopic forces is proposed in place of the skew-symmetric
interconnection submatrix. Reduction of the number of matching partial
differential equations in IDA-PBC and simplification of the structure of the
matching partial differential equations are achieved by eliminating the
gyroscopic force from the matching partial differential equations. In addition,
easily verifiable criteria are provided for Lyapunov/exponential
stabilizability by IDA-PBC for all linear controlled Hamiltonian systems with
arbitrary degrees of underactuation and for all nonlinear controlled
Hamiltonian systems with one degree of underactuation. A general design
procedure for IDA-PBC is given and illustrated with examples. The duality of
the new IDA-PBC method to the method of controlled Lagrangians is discussed.
This paper renders the IDA-PBC method as powerful as the controlled Lagrangian
method
A Popov Stability Condition for Uncertain Linear Quantum Systems
This paper considers a Popov type approach to the problem of robust stability
for a class of uncertain linear quantum systems subject to unknown
perturbations in the system Hamiltonian. A general stability result is given
for a general class of perturbations to the system Hamiltonian. Then, the
special case of a nominal linear quantum system is considered with quadratic
perturbations to the system Hamiltonian. In this case, a robust stability
condition is given in terms of a frequency domain condition which is of the
same form as the standard Popov stability condition.Comment: A shortened version to appear in the proceedings of the 2013 American
Control Conferenc
Reduction of Second-Order Network Systems with Structure Preservation
This paper proposes a general framework for structure-preserving model
reduction of a secondorder network system based on graph clustering. In this
approach, vertex dynamics are captured by the transfer functions from inputs to
individual states, and the dissimilarities of vertices are quantified by the
H2-norms of the transfer function discrepancies. A greedy hierarchical
clustering algorithm is proposed to place those vertices with similar dynamics
into same clusters. Then, the reduced-order model is generated by the
Petrov-Galerkin method, where the projection is formed by the characteristic
matrix of the resulting network clustering. It is shown that the simplified
system preserves an interconnection structure, i.e., it can be again
interpreted as a second-order system evolving over a reduced graph.
Furthermore, this paper generalizes the definition of network controllability
Gramian to second-order network systems. Based on it, we develop an efficient
method to compute H2-norms and derive the approximation error between the
full-order and reduced-order models. Finally, the approach is illustrated by
the example of a small-world network
Matching in the method of controlled Lagrangians and IDA-passivity based control
This paper reviews the method of controlled Lagrangians and the interconnection and damping assignment passivity based control (IDA-PBC)method. Both methods have been presented recently in the literature as means to stabilize a desired equilibrium point of an Euler-Lagrange system, respectively Hamiltonian system, by searching for a stabilizing structure preserving feedback law. The conditions under which two Euler-Lagrange or Hamiltonian systems are equivalent under feedback are called the matching conditions (consisting of a set of nonlinear PDEs). Both methods are applied to the general class of underactuated mechanical systems and it is shown that the IDA-PBC method contains the controlled Lagrangians method as a special case by choosing an appropriate closed-loop interconnection structure. Moreover, explicit conditions are derived under which the closed-loop Hamiltonian system is integrable, leading to the introduction of gyroscopic terms. The -method as introduced in recent papers for the controlled Lagrangians method transforms the matching conditions into a set of linear PDEs. In this paper the method is extended, transforming the matching conditions obtained in the IDA-PBC method into a set of quasi-linear and linear PDEs.\u
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