arXiv subjects

Gian Giacomo Guerreschi

Publications and source records attributed to Gian Giacomo Guerreschi.

31 records · Page 2Linked to original sources

arXiv2018

Repeat-Until-Success circuits with fixed-point oblivious amplitude amplification

Certain quantum operations can be built more efficiently through a procedure known as Repeat-Until-Success. Differently from other non-deterministic quantum operations, this procedure provides a classical flag which certifies the success or failure of the procedure and, in the latter case, a recovery step allows the restoration of the quantum state to its original condition. The procedure can then be repeated until success is achieved. After success is certified, the RUS procedure can be equated to a coherent gate. However, this is not the case when the operation needs to be conditioned on the state of other qubits, possibly being in a superposition state. In this situation, the final operation depends on the failure and success history and introduces a "distortion" that, even after the final success, depends on the past outcomes. We quantify the distortion and show that it can be reduced by increasing the probability of success towards unity. While this can be achieved via oblivious amplitude amplification when the initial success probability is known, we propose the use of fixed-point oblivious amplitude amplification to reduce this unwanted distortions below any given threshold even without knowing the initial success probability.

quant-ph↗

arXiv2018

Two-step approach to scheduling quantum circuits

As the effort to scale up existing quantum hardware proceeds, it becomes necessary to schedule quantum gates in a way that minimizes the number of operations. There are three constraints that have to be satisfied: the order or dependency of the quantum gates in the specific algorithm, the fact that any qubit may be involved in at most one gate at a time, and the restriction that two-qubit gates are implementable only between connected qubits. The last aspect implies that the compilation depends not only on the algorithm, but also on hardware properties like connectivity. Here we suggest a two-step approach in which logical gates are initially scheduled neglecting connectivity considerations, while routing operations are added at a later step in a way that minimizes their overhead. We rephrase the subtasks of gate scheduling in terms of graph problems like edge-coloring and maximum subgraph isomorphism. While this approach is general, we specialize to a one dimensional array of qubits to propose a routing scheme that is minimal in the number of exchange operations. As a practical application, we schedule the Quantum Approximate Optimization Algorithm in a linear geometry and quantify the reduction in the number of gates and circuit depth that results from increasing the efficacy of the scheduling strategies.

quant-ph↗

arXiv2017

Quantum Neuron: an elementary building block for machine learning on quantum computers

Even the most sophisticated artificial neural networks are built by aggregating substantially identical units called neurons. A neuron receives multiple signals, internally combines them, and applies a non-linear function to the resulting weighted sum. Several attempts to generalize neurons to the quantum regime have been proposed, but all proposals collided with the difficulty of implementing non-linear activation functions, which is essential for classical neurons, due to the linear nature of quantum mechanics. Here we propose a solution to this roadblock in the form of a small quantum circuit that naturally simulates neurons with threshold activation. Our quantum circuit defines a building block, the "quantum neuron", that can reproduce a variety of classical neural network constructions while maintaining the ability to process superpositions of inputs and preserve quantum coherence and entanglement. In the construction of feedforward networks of quantum neurons, we provide numerical evidence that the network not only can learn a function when trained with superposition of inputs and the corresponding output, but that this training suffices to learn the function on all individual inputs separately. When arranged to mimic Hopfield networks, quantum neural networks exhibit properties of associative memory. Patterns are encoded using the simple Hebbian rule for the weights and we demonstrate attractor dynamics from corrupted inputs. Finally, the fact that our quantum model closely captures (traditional) neural network dynamics implies that the vast body of literature and results on neural networks becomes directly relevant in the context of quantum machine learning.

quant-ph↗

arXiv2017

Practical optimization for hybrid quantum-classical algorithms

A novel class of hybrid quantum-classical algorithms based on the variational approach have recently emerged from separate proposals addressing, for example, quantum chemistry and combinatorial problems. These algorithms provide an approximate solution to the problem at hand by encoding it in the state of a quantum computer. The operations used to prepare the state are not a priori fixed but, quite the opposite, are subjected to a classical optimization procedure that modifies the quantum gates and improves the quality of the approximate solution. While the quantum hardware determines the size of the problem and what states are achievable (limited, respectively, by the number of qubits and by the kind and number of possible quantum gates), it is the classical optimization procedure that determines the way in which the quantum states are explored and whether the best available solution is actually reached. In addition, the quantities required in the optimization, for example the objective function itself, have to be estimated with finite precision in any experimental implementation. While it is desirable to have very precise estimates, this comes at the cost of repeating the state preparation and measurement multiple times. Here we analyze the competing requirements of high precision and low number of repetitions and study how the overall performance of the variational algorithm is affected by the precision level and the choice of the optimization method. Finally, this study introduces quasi-Newton optimization methods in the general context of hybrid variational algorithms and presents quantitative results for the Quantum Approximate Optimization Algorithm.

quant-ph↗

arXiv2016

Faster than Classical Quantum Algorithm for dense Formulas of Exact Satisfiability and Occupation Problems

We present an exact quantum algorithm for solving the Exact Satisfiability (XSAT) problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts: First, the identification and efficient characterization of a restricted subspace that contains all the valid assignments of the XSAT; Second, a quantum search in such restricted subspace. The quantum algorithm can be used either to find a valid assignment (or to certify that no solution exists) or to count the total number of valid assignments. The query complexities for the worst-case are respectively bounded by $O(\sqrt{2^{n-M^{\prime}}})$ and $O(2^{n-M^{\prime}})$, where $n$ is the number of variables and $M^{\prime}$ the number of linearly independent clauses. Remarkably, the proposed quantum algorithm results to be faster than any known exact classical algorithm to solve dense formulas of XSAT. As a concrete application, we provide the worst-case complexity for the Hamiltonian cycle problem obtained after mapping it to a suitable XSAT. Specifically, we show that the time complexity for the proposed quantum algorithm is bounded by $O(2^{n/4})$ for 3-regular undirected graphs, where $n$ is the number of nodes. The same worst-case complexity holds for $(3,3)$-regular bipartite graphs (the current best classical algorithm has a (worst-case) running time bounded by $O(2^{31n/96})$). Finally, when compared to heuristic techniques for XSAT, the proposed quantum algorithm is faster than the classical WalkSAT and Adiabatic Quantum Optimization for random instances with a density of constraints close to the satisfiability threshold, the regime in which instances are typically the hardest to solve. The proposed quantum algorithm can be also extended to the generalized version of the XSAT known as Occupation problem.

quant-ph↗

arXiv2015

Adiabatic quantum optimization in presence of discrete noise: Reducing the problem dimensionality

Adiabatic quantum optimization is a procedure to solve a vast class of optimization problems by slowly changing the Hamiltonian of a quantum system. The evolution time necessary for the algorithm to be successful scales inversely with the minimum energy gap encountered during the dynamics. Unfortunately, the direct calculation of the gap is strongly limited by the exponential growth in the dimensionality of the Hilbert space associated to the quantum system. Although many special-purpose methods have been devised to reduce the effective dimensionality, they are strongly limited to particular classes of problems with evident symmetries. Moreover, little is known about the computational power of adiabatic quantum optimizers in real-world conditions. Here, we propose and implement a general purposes reduction method that does not rely on any explicit symmetry and which requires, under certain general conditions, only a polynomial amount of classical resources. Thanks to this method, we are able to analyze the performance of "non-ideal" quantum adiabatic optimizers to solve the well-known Grover problem, namely the search of target entries in an unsorted database, in the presence of discrete local defects. In this case, we show that adiabatic quantum optimization, even if affected by random noise, is still potentially faster than any classical algorithm.

quant-ph↗

arXiv2015

Microwave Boson Sampling

The first post-classical computation will most probably be performed not on a universal quantum computer, but rather on a dedicated quantum hardware. A strong candidate for achieving this is represented by the task of sampling from the output distribution of linear quantum optical networks. This problem, known as boson sampling, has recently been shown to be intractable for any classical computer, but it is naturally carried out by running the corresponding experiment. However, only small scale realizations of boson sampling experiments have been demonstrated to date. Their main limitation is related to the non-deterministic state preparation and inefficient measurement step. Here, we propose an alternative setup to implement boson sampling that is based on microwave photons and not on optical photons. The certified scalability of superconducting devices indicates that this direction is promising for a large-scale implementation of boson sampling and allows for more flexible features like arbitrary state preparation and efficient photon-number measurements.

quant-ph↗

arXiv2014

Boson Sampling for Molecular Vibronic Spectra

Quantum computers are expected to be more efficient in performing certain computations than any classical machine. Unfortunately, the technological challenges associated with building a full-scale quantum computer have not yet allowed the experimental verification of such an expectation. Recently, boson sampling has emerged as a problem that is suspected to be intractable on any classical computer, but efficiently implementable with a linear quantum optical setup. Therefore, boson sampling may offer an experimentally realizable challenge to the Extended Church-Turing thesis and this remarkable possibility motivated much of the interest around boson sampling, at least in relation to complexity-theoretic questions. In this work, we show that the successful development of a boson sampling apparatus would not only answer such inquiries, but also yield a practical tool for difficult molecular computations. Specifically, we show that a boson sampling device with a modified input state can be used to generate molecular vibronic spectra, including complicated effects such as Duschinsky rotations.

quant-ph↗

arXiv2013

Multiple re-encounter approach to radical pair reactions and the role of nonlinear master equations

We formulate a multiple-encounter model of the radical pair mechanism that is based on a random coupling of the radical pair to a minimal model environment. These occasional pulse-like couplings correspond to the radical encounters and give rise to both dephasing and recombination. While this is in agreement with the original model of Haberkorn and its extensions that assume additional dephasing, we show how a nonlinear master equation may be constructed to describe the conditional evolution of the radical pairs prior to the detection of their recombination. We propose a nonlinear master equation for the evolution of an ensemble of independently evolving radical pairs whose nonlinearity depends on the record of the fluorescence signal. We also reformulate Haberkorn's original argument on the physicality of reaction operators using the terminology of quantum optics/open quantum systems. Our model allows one to describe multiple encounters within the exponential model and connects this with the master equation approach. We include hitherto neglected effects of the encounters, such as a separate dephasing in the triplet subspace, and predict potential new effects, such as Grover reflections of radical spins, that may be observed if the strength and time of the encounters can be experimentally controlled.

quant-ph↗

arXiv2012

Optical switching of radical pair conformation enhances magnetic sensitivity

The yield of chemical reactions involving intermediate radical pairs is influenced by magnetic fields well beyond the levels expected from energy considerations. This dependence can be traced back to the microscopic dynamics of electron spins and constitutes the basis of the chemical compass. Here we propose a new experimental approach based on molecular photoswitches to achieve additional control on the chemical reaction and to allow short-time resolution of the spin dynamics. Our proposal enables experiments to test some of the standard assumptions of the radical pair model and improves the sensitivity of chemical magnetometers by two orders of magnitude.

physics.bio-ph↗

arXiv2011

Persistent dynamic entanglement from classical motion: How bio-molecular machines can generate non-trivial quantum states

Very recently [Phys. Rev. E 82, 021921 (2010)] a simple mechanism was presented by which a molecule subjected to forced oscillations, out of thermal equilibrium, can maintain quantum entanglement between two of its quantum degrees of freedom. Crucially, entanglement can be maintained even in the presence of very intense noise, so intense that no entanglement is possible when the forced oscillations cease. This mechanism may allow for the presence of non-trivial quantum entanglement in biological systems. Here we significantly enlarge the study of this model. In particular, we show that the persistent generation of dynamic entanglement is not restricted to the bosonic heat bath model, but it can also be observed in other decoherence models, e.g. the spin gas model, and in non-Markovian scenarios. We also show how conformational changes can be used by an elementary machine to generate entanglement even in unfavorable conditions. In biological systems, similar mechanisms could be exploited by more complex molecular machines or motors.

quant-ph↗

arXiv2010

Motional effects on the efficiency of excitation transfer

Energy transfer plays a vital role in many natural and technological processes. In this work, we study the effects of mechanical motion on the excitation transfer through a chain of interacting molecules with application to biological scenarios of transfer processes. Our investigation demonstrates that, for various types of mechanical oscillations, the transfer efficiency is significantly enhanced over that of comparable static configurations. This enhancement is a genuine quantum signature, and requires the collaborative interplay between the quantum-coherent evolution of the excitation and the mechanical motion of the molecules; it has no analogue in the classical incoherent energy transfer. This effect may not only occur naturally, but it could be exploited in artificially designed systems to optimize transport processes. As an application, we discuss a simple and hence robust control technique.

quant-ph↗

arXiv2010

Quantum control and entanglement in a chemical compass

The radical pair mechanism is one of the two main hypotheses to explain the navigability of animals in weak magnetic fields, enabling e.g. birds to see the Earth's magnetic field. It also plays an essential role in the field of spin chemistry. Here, we show how quantum control can be used to either enhance or reduce the performance of such a chemical compass, providing a new route to further study the radical pair mechanism and its applications. We study the role of quantum entanglement in this mechanism, and demonstrate intriguing connections between radical-pair entanglement and the magnetic field sensitivity of the compass. Beyond their immediate application to the radical pair mechanism, these results also demonstrate how state-of-the-art quantum technologies could potentially be used to probe and control biological functions.

quant-ph↗