Related papers: Relating computational complexity and quantum spec…
We analyze the influence of errors on the implementation of the quantum Fourier transformation (QFT) on the Ising quantum computer (IQC). Two kinds of errors are studied: (i) due to spurious transitions caused by pulses and (ii) due to…
Partly on the basis of heuristic arguments from physics it has been suggested that the performance of certain types of algorithms on random $k$-SAT formulas is linked to phase transitions that affect the geometry of the set of satisfying…
We study the fluctuation properties of transition intensities applying a recently proposed generalization of the random matrix theory, which is based on Beck and Cohen's superstatistics. We obtain an analytic expression for the distribution…
Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely…
The statistics of S-matrix fluctuations are numerically investigated on a model for irregular quantum scattering in which a classical chaotic diffusion takes place within the interaction region. Agreement with various random-matrix…
One way to look for complex behaviours in many-body quantum systems is to let the number $N$ of degrees of freedom become large and focus upon collective observables. Mean-field quantities scaling as $1/N$ tend to commute, whence complexity…
Using a novel approach, we investigate the shape of the average spectrum and the spectral fluctuations of the $k$-body embedded unitary ensemble in the limit of large matrix dimension. We identify the transition point between semicircle and…
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update…
Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-rigorous statistical mechanics ideas have inspired a message passing algorithm called Belief Propagation Guided Decimation for finding satisfying…
Quantum satisfiability is a constraint satisfaction problem that generalizes classical boolean satisfiability. In the quantum k-SAT problem, each constraint is specified by a k-local projector and is satisfied by any state in its nullspace.…
A fundamental question in Computer Science is understanding when a specific class of problems go from being computationally easy to hard. Because of its generality and applications, the problem of Boolean Satisfiability (aka SAT) is often…
Quantum analogues of the transient fluctuation theorem(TFT) and steady-state fluctuation theorem(SSFT) are investigated for a harmonic oscillator linearly coupled with a harmonic reservoir. The probability distribution for the work done…
The concept of statistical complexity is studied to characterize the classical kicked top model which plays important role in the qbit systems and the chaotic properties of the entanglement. This allows us to understand this driven…
We describe the transport properties of a point contact under the influence of a classical two-level fluctuator. We employ a transfer matrix formalism allowing us to calculate arbitrary correlation functions of the stochastic process by…
We study the connection between the order of phase transitions in combinatorial problems and the complexity of decision algorithms for such problems. We rigorously show that, for a class of random constraint satisfaction problems, a limited…
This paper combines probabilistic and algebraic techniques for computing quantum expectations of operator exponentials (and their products) of quadratic forms of quantum variables in Gaussian states. Such quadratic-exponential functionals…
Recently it was shown that the main distinguishing features of quantum mechanics (QM) can be reproduced by a model based on classical random fields, so called prequantum classical statistical field theory (PCSFT). This model provides a…
The (2+p)-Satisfiability (SAT) problem interpolates between different classes of complexity theory and is believed to be of basic interest in understanding the onset of typical case complexity in random combinatorics. In this paper, a…
We study a fragmentation problem where an initial object of size x is broken into m random pieces provided x>x_0 where x_0 is an atomic cut-off. Subsequently the fragmentation process continues for each of those daughter pieces whose sizes…
A new quantum algorithm is proposed to solve Satisfiability(SAT) problems by taking advantage of non-unitary transformation in ground state quantum computer. The energy gap scale of the ground state quantum computer is analyzed for 3-bit…