Papers by Federico Spedalieri
IEEE Transactions on Nanotechnology, May 1, 2011
Quantum Information & Computation, Jul 1, 2009
Scientific Reports
We present a very general construction for quantum annealing protocols to solve Combinational Cir... more We present a very general construction for quantum annealing protocols to solve Combinational Circuit Fault Diagnosis problems that restricts the evolution to the space of valid diagnoses. This is accomplished by using special local drivers that induce a transition graph on the space of feasible configurations that is regular and instance independent for each given circuit topology. Analysis of small instances shows that the energy gap has a generic form, and that the minimum gap occurs in the last third of the evolution. We used these features to construct an improved annealing schedule and benchmarked its performance through closed system simulations. We found that degeneracy can help the performance of quantum annealing, especially for instances with a higher number of faults in their minimum fault diagnosis. This contrasts with the performance of classical approaches based on brute force search that are used in industry for large scale circuits.
We show how to design families of operational criteria that distinguish entangled from separable ... more We show how to design families of operational criteria that distinguish entangled from separable quantum states. The simplest of these tests corresponds to the well-known Peres-Horodecki positive partial transpose (PPT) criterion, and the more complicated tests are strictly stronger. The new criteria are tractable due to powerful computational and theoretical methods for the class of convex optimization problems known as semidefinite programs. We successfully applied the results to many low-dimensional states from the literature where the PPT test fails. As a byproduct of the criteria, we provide an explicit construction of the corresponding entanglement witnesses.
Quantum Science and Technology, 2021
Recent advances in the field of adiabatic quantum computing and the closely related field of quan... more Recent advances in the field of adiabatic quantum computing and the closely related field of quantum annealing have centered around using more advanced and novel Hamiltonian representations to solve optimization problems. One of these advances has centered around the development of driver Hamiltonians that commute with the constraints of an optimization problem—allowing for another avenue to satisfying those constraints instead of imposing penalty terms for each of them. In particular, the approach is able to use sparser connectivity to embed several practical problems on quantum devices in comparison to the standard approach of using penalty terms. However, designing the driver Hamiltonians that successfully commute with several constraints has largely been based on strong intuition for specific problems and with no simple general algorithm for generating them for arbitrary constraints. In this work, we develop a simple and intuitive algebraic framework for reasoning about the comm...
Entropy, 2020
Boltzmann machines have useful roles in deep learning applications, such as generative data model... more Boltzmann machines have useful roles in deep learning applications, such as generative data modeling, initializing weights for other types of networks, or extracting efficient representations from high-dimensional data. Most Boltzmann machines use restricted topologies that exclude looping connectivity, as such connectivity creates complex distributions that are difficult to sample. We have used an open-system quantum annealer to sample from complex distributions and implement Boltzmann machines with looping connectivity. Further, we have created policies mapping Boltzmann machine variables to the quantum bits of an annealer. These policies, based on correlation and entropy metrics, dynamically reconfigure the topology of Boltzmann machines during training and improve performance.
ACM Journal on Emerging Technologies in Computing Systems, 2018
Current deep learning approaches have been very successful using convolutional neural networks tr... more Current deep learning approaches have been very successful using convolutional neural networks trained on large graphical-processing-unit-based computers. Three limitations of this approach are that (1) they are based on a simple layered network topology, i.e., highly connected layers, without intra-layer connections; (2) the networks are manually configured to achieve optimal results, and (3) the implementation of the network model is expensive in both cost and power. In this article, we evaluate deep learning models using three different computing architectures to address these problems: quantum computing to train complex topologies, high performance computing to automatically determine network topology, and neuromorphic computing for a low-power hardware implementation. We use the MNIST dataset for our experiment, due to input size limitations of current quantum computers. Our results show the feasibility of using the three architectures in tandem to address the above deep learni...
Entropy, 2018
Training deep learning networks is a difficult task due to computational complexity, and this is ... more Training deep learning networks is a difficult task due to computational complexity, and this is traditionally handled by simplifying network topology to enable parallel computation on graphical processing units (GPUs). However, the emergence of quantum devices allows reconsideration of complex topologies. We illustrate a particular network topology that can be trained to classify MNIST data (an image dataset of handwritten digits) and neutrino detection data using a restricted form of adiabatic quantum computation known as quantum annealing performed by a D-Wave processor. We provide a brief description of the hardware and how it solves Ising models, how we translate our data into the corresponding Ising models, and how we use available expanded topology options to explore potential performance improvements. Although we focus on the application of quantum annealing in this article, the work discussed here is just one of three approaches we explored as part of a larger project that considers alternative means for training deep learning networks. The other approaches involve using a high performance computing (HPC) environment to automatically find network topologies with good performance and using neuromorphic computing to find a low-power solution for training deep learning networks. Our results show that our quantum approach can find good network parameters in a reasonable time despite increased network topology complexity; that HPC can find good parameters for traditional, simplified network topologies; and that neuromorphic computers can use low power memristive hardware to represent complex topologies and parameters derived from other architecture choices.
Using Government drawings, specifications, or other data included in this document for any purpos... more Using Government drawings, specifications, or other data included in this document for any purpose other than Government procurement does not in any way obligate the U.S. Government. The fact that the Government formulated or supplied the drawings, specifications, or other data does not license the holder or any other person or corporation; or convey any rights or permission to manufacture, use, or sell any patented invention that may relate to them. This report is the result of contracted fundamental research deemed exempt from public affairs security and policy review in accordance with SAF/AQR memorandum dated 10 Dec 08 and AFRL/CA policy clarification memorandum dated 16 Jan 09. This report is available to the general public, including foreign nationals. Copies may be obtained from the Defense Technical Information Center (DTIC) (http://www.dtic.mil).
Physical Review Applied, 2016
Recent advances in quantum technology have led to the development and manufacturing of experiment... more Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealers that promise to solve certain combinatorial optimization problems of practical relevance faster than their classical analogues. The applicability of such devices for many theoretical and real-world optimization problems, which are often constrained, is severely limited by the sparse, rigid layout of the devices' quantum bits. Traditionally, constraints are addressed by the addition of penalty terms to the Hamiltonian of the problem, which in turn requires prohibitively increasing physical resources while also restricting the dynamical range of the interactions. Here, we propose a method for encoding constrained optimization problems on quantum annealers that eliminates the need for penalty terms and thereby reduces the number of required couplers and removes the need for minor embedding, greatly reducing the number of required physical qubits. We argue the advantages of the proposed technique and illustrate its effectiveness. We conclude by discussing the experimental feasibility of the suggested method as well as its potential to appreciably reduce the resource requirements for implementing optimization problems on quantum annealers, and its significance in the field of quantum computing.
Physical Review A, 2015
A recent experiment [Lanting et al., PRX, (2014)] claimed to provide evidence of up to 8-qubit en... more A recent experiment [Lanting et al., PRX, (2014)] claimed to provide evidence of up to 8-qubit entanglement in a D-Wave quantum annealing device. However, entanglement was measured using qubit tunneling spectroscopy, a technique that provides indirect access to the state of the system at intermediate times during the anneal by performing measurements at the end of the anneal with a probe qubit. In addition, an underlying assumption was that the quantum transverse-field Ising Hamiltonian, whose ground states are already highly entangled, is an appropriate model of the device, and not some other (possibly classical) model. This begs the question of whether alternative, classical or semiclassical models would be equally effective at predicting the observed spectrum and thermal state populations. To check this, we consider a recently proposed classical rotor model with classical Monte Carlo updates, which has been successfully employed in describing features of earlier experiments involving the device. We also consider simulated quantum annealing with quantum Monte Carlo updates, an algorithm that samples from the instantaneous Gibbs state of the device Hamiltonian. Finally, we use the quantum adiabatic master equation, which cannot be efficiently simulated classically, and which has previously been used to successfully capture the open system quantum dynamics of the device. We find that only the master equation is able to reproduce the features of the tunneling spectroscopy experiment, while both the classical rotor model and simulated quantum annealing fail to reproduce the experimental results. We argue that this bolsters the evidence for the reported entanglement.
Scientific Reports, 2014
Two objects can be distinguished if they have different measurable properties. Thus, distinguisha... more Two objects can be distinguished if they have different measurable properties. Thus, distinguishability depends on the Physics of the objects. In considering graphs, we revisit the Ising model as a framework to define physically meaningful spectral invariants. In this context, we introduce a family of refinements of the classical spectrum and consider the quantum partition function. We demonstrate that the energy spectrum of the quantum Ising Hamiltonian is a stronger invariant than the classical one without refinements. For the purpose of implementing the related physical systems, we perform experiments on a programmable annealer with superconducting flux technology. Departing from the paradigm of adiabatic computation, we take advantage of a noisy evolution of the device to generate statistics of low energy states. The graphs considered in the experiments have the same classical partition functions, but different quantum spectra. The data obtained from the annealer distinguish non...
Frontiers in Optics, 2006
We design a controlled-phase gate for linear optical quantum computing by using photodetectors th... more We design a controlled-phase gate for linear optical quantum computing by using photodetectors that cannot resolve photon number. An intrinsic error-correction circuit corrects errors introduced by the detectors. Our controlled-phase gate has a 1/4 success probability. Recent development in cluster-state quantum computing has shown that a two-qubit gate with non-zero success probability can build an arbitrarily large cluster state with only polynomial overhead. Hence, it is possible to generate optical cluster states without number-resolving detectors and with polynomial overhead.
Physical Review Letters, 2002
Physical Review D, 1995
A primordial magnetic field may be generated during an inflationary period if conformal invarianc... more A primordial magnetic field may be generated during an inflationary period if conformal invariance is broken. We reexamine and generalize previous results about the magnetic field produced by couplings of the form R n F µν F µν. We show that the amplitude of the magnetic field depends strongly on n. For adequate values of n the field produced can serve as seed for galactic magnetic fields. We also compute the effective interaction between the electromagnetic field and the geometry in the context of scalar QED (with and without classical conformal invariance). In both cases, the amplitude of the magnetic field is too small to be of astrophysical interest.
Physical Review A, 2005
We discuss the problem of determining whether the state of several quantum mechanical subsystems ... more We discuss the problem of determining whether the state of several quantum mechanical subsystems is entangled. As in previous work on two subsystems we introduce a procedure for checking separability that is based on finding state extensions with appropriate properties and may be implemented as a semidefinite program. The main result of this work is to show that there is a series of tests of this kind such that if a multiparty state is entangled this will eventually be detected by one of the tests. The procedure also provides a means of constructing entanglement witnesses that could in principle be measured in order to demonstrate that the state is entangled.
Physical Review A, 2006
We show that the KLM scheme [Knill, Laflamme and Milburn, Nature 409, 46] can be implemented usin... more We show that the KLM scheme [Knill, Laflamme and Milburn, Nature 409, 46] can be implemented using polarization encoding, thus reducing the number of path modes required by half. One of the main advantages of this new implementation is that it naturally incorporates a loss detection mechanism that makes the probability of a gate introducing a non-detected error, when non-ideal detectors are considered, dependent only on the detector dark-count rate and independent of its efficiency. Since very low dark-count rate detectors are currently available, a high-fidelity gate (probability of error of order 10 −6 conditional on the gate being successful) can be implemented using polarization encoding. The detector efficiency determines the overall success probability of the gate but does not affect its fidelity. This can be applied to the efficient construction of optical cluster states with very high fidelity for quantum computing.
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Papers by Federico Spedalieri