Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userL0 regularization-based compressed sensing with quantum-classical hybrid approach
78
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
L0-regularization-based compressed sensing (L0-RBCS) is capable of outperforming L1-RBCS, but it is difficult to solve an optimization problem for L0-RBCS that cannot be formulated as a convex optimization. To achieve the optimization for L0-RBCS, we propose a quantum-classical hybrid system consisting of a quantum machine and a classical digital processor. Because forming a densely-connected network on a quantum machine is required for solving this problem, the coherent Ising machine (CIM) is one of suitable quantum machines for composing this hybrid system. To evaluate theoretically the performance of the CIM-classical hybrid system, a truncated Wigner stochastic differential equation (W-SDE) is obtained from the master equation for the density operator of the network of degenerate optical parametric oscillators, and macroscopic equations are derived from the W-SDE using statistical mechanics. We show that the system performance in principle approaches the theoretical limit of compressed sensing and in practical situations this hybrid system can exceed L1-RBCSs estimation accuracy.
rate research
Read More
We generalize the classical shadow tomography scheme to a broad class of finite-depth or finite-time local unitary ensembles, known as locally scrambled quantum dynamics, where the unitary ensemble is invariant under local basis transformations. In this case, the reconstruction map for the classical shadow tomography depends only on the average entanglement feature of classical snapshots. We provide an unbiased estimator of the quantum state as a linear combination of reduced classical snapshots in all subsystems, where the combination coefficients are solely determined by the entanglement feature. We also bound the number of experimental measurements required for the tomography scheme, so-called sample complexity, by formulating the operator shadow norm in the entanglement feature formalism. We numerically demonstrate our approach for finite-depth local unitary circuits and finite-time local-Hamiltonian generated evolutions. The shallow-circuit measurement can achieve a lower tomography complexity compared to the existing method based on Pauli or Clifford measurements. Our approach is also applicable to approximately locally scrambled unitary ensembles with a controllable bias that vanishes quickly. Surprisingly, we find a single instance of time-dependent local Hamiltonian evolution is sufficient to perform an approximate tomography as we numerically demonstrate it using a paradigmatic spin chain Hamiltonian modeled after trapped ion or Rydberg atom quantum simulators. Our approach significantly broadens the application of classical shadow tomography on near-term quantum devices.
Many interesting problems in fields ranging from telecommunications to computational biology can be formalized in terms of large underdetermined systems of linear equations with additional constraints or regularizers. One of the most studied ones, the Compressed Sensing problem (CS), consists in finding the solution with the smallest number of non-zero components of a given system of linear equations $boldsymbol y = mathbf{F} boldsymbol{w}$ for known measurement vector $boldsymbol{y}$ and sensing matrix $mathbf{F}$. Here, we will address the compressed sensing problem within a Bayesian inference framework where the sparsity constraint is remapped into a singular prior distribution (called Spike-and-Slab or Bernoulli-Gauss). Solution to the problem is attempted through the computation of marginal distributions via Expectation Propagation (EP), an iterative computational scheme originally developed in Statistical Physics. We will show that this strategy is comparatively more accurate than the alternatives in solving instances of CS generated from statistically correlated measurement matrices. For computational strategies based on the Bayesian framework such as variants of Belief Propagation, this is to be expected, as they implicitly rely on the hypothesis of statistical independence among the entries of the sensing matrix. Perhaps surprisingly, the method outperforms uniformly also all the other state-of-the-art methods in our tests.
Classical models with complex energy landscapes represent a perspective avenue for the near-term application of quantum simulators. Until now, many theoretical works studied the performance of quantum algorithms for models with a unique ground state. However, when the classical problem is in a so-called clustering phase, the ground state manifold is highly degenerate. As an example, we consider a 3-XORSAT model defined on simple hypergraphs. The degeneracy of classical ground state manifold translates into the emergence of an extensive number of $Z_2$ symmetries, which remain intact even in the presence of a quantum transverse magnetic field. We establish a general duality approach that restricts the quantum problem to a given sector of conserved $Z_2$ charges and use it to study how the outcome of the quantum adiabatic algorithm depends on the hypergraph geometry. We show that the tree hypergraph which corresponds to a classically solvable instance of the 3-XORSAT problem features a constant gap, whereas the closed hypergraph encounters a second-order phase transition with a gap vanishing as a power-law in the problem size. The duality developed in this work provides a practical tool for studies of quantum models with classically degenerate energy manifold and reveals potential connections between glasses and gauge theories.
Finding the global minimum in a rugged potential landscape is a computationally hard task, often equivalent to relevant optimization problems. Simulated annealing is a computational technique which explores the configuration space by mimicking thermal noise. By slow cooling, it freezes the system in a low-energy configuration, but the algorithm often gets stuck in local minima. In quantum annealing, the thermal noise is replaced by controllable quantum fluctuations, and the technique can be implemented in modern quantum simulators. However, quantum-adiabatic schemes become prohibitively slow in the presence of quasidegeneracies. Here we propose a strategy which combines ideas from simulated annealing and quantum annealing. In such hybrid algorithm, the outcome of a quantum simulator is processed on a classical device. While the quantum simulator explores the configuration space by repeatedly applying quantum fluctuations and performing projective measurements, the classical computer evaluates each configuration and enforces a lowering of the energy. We have simulated this algorithm for small instances of the random energy model, showing that it potentially outperforms both simulated thermal annealing and adiabatic quantum annealing. It becomes most efficient for problems involving many quasi-degenerate ground states.
We study the effects of power-law long-range couplings on measurement-induced phases and transitions in tractable large-$N$ models, including a Brownian qubit model and a Brownian SYK model. In one dimension, the long-range coupling is irrelevant for $alpha>3/2$, with $alpha$ being the power-law exponent, thus the volume-law and area-law entanglement phases and the phase transition remain intact. For $alpha<3/2$ the long-range coupling becomes relevant, leading to a nontrivial dynamical exponent at the measurement-induced phase transition. More interestingly, for $alpha<1$ the entanglement pattern receives a sub-volume correction for both area-law and volume-law phases. The volume-law phase with such a sub-volume correction realizes a novel quantum error correcting code whose code distance scales as $L^{2-2alpha}$. We further extend the calculation to a quadratic SYK model, where two distinct fractal entangled phases emerge, leading to a complete phase diagram of the long-range free fermion model under monitoring.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
