arXiv subjects

Isaac Chuang

Publications and source records attributed to Isaac Chuang.

At least 37 records · Page 2Linked to original sources

arXiv2020

Operating Characteristics for Binary Hypothesis Testing in Quantum Systems

Receiver operating characteristics (ROCs) are a well-established representation of the tradeoff between detection and false alarm probabilities in classical binary hypothesis testing. We use classical ROCs as motivation for two types of operating characteristics for binary hypothesis testing in quantum systems -- decision operating characteristics (QDOCs) and measurement operating characteristics (QMOCs). Both are described in the context of a framework we propose that encompasses the typical formulations of binary hypothesis testing in both the classical and quantum scenarios. We interpret Helstrom's well-known result regarding discrimination between two quantum density operators with minimum probability of error in this framework. We also present a generalization of previous results regarding the correspondence between classical Parseval frames and quantum measurements. The derivation naturally leads to a constructive procedure for generating many different measurements besides Helstrom's optimal measurement, some standard and others non-standard, that achieve minimum probability of error.

quant-ph↗

arXiv2020

IP Geolocation Underestimates Regressive Economic Patterns in MOOC Usage

Massive open online courses (MOOCs) promise to make rigorous higher education accessible to everyone, but prior research has shown that registrants tend to come from backgrounds of higher socioeconomic status. We study geographically granular economic patterns in about 76,000 U.S. registrations for about 600 HarvardX and MITx courses between 2012 and 2018, identifying registrants' locations using both IP geolocation and user-reported mailing addresses. By either metric, we find higher registration rates among postal codes with greater prosperity or population density. However, we also find evidence of bias in IP geolocation: it makes greater errors, both geographically and economically, for users from more economically distressed areas; it disproportionately places users in prosperous areas; and it underestimates the regressive pattern in MOOC registration. Researchers should use IP geolocation in MOOC studies with care, and consider the possibility of similar economic biases affecting its other academic, commercial, and legal uses.

cs.CY↗

arXiv2020

Modelling and Using Response Times in Online Courses

Each time a learner in a self-paced online course seeks to answer an assessment question, it takes some time for the student to read the question and arrive at an answer to submit. If multiple attempts are allowed, and the first answer is incorrect, it takes some time to provide a second answer. Here we study the distribution of such "response times." We find that the log-normal statistical model for such times, previously suggested in the literature, holds for online courses. Users who, according to this model, tend to take longer on submits are more likely to complete the course, have a higher level of engagement, and achieve a higher grade. This finding can be the basis for designing interventions in online courses, such as MOOCs, which would encourage "fast" users to slow down.

cs.HC↗

arXiv2019

Empirical determination of the simulation capacity of a near-term quantum computer

Experimentally realizable quantum computers are rapidly approaching the threshold of quantum supremacy. Quantum Hamiltonian simulation promises to be one of the first practical applications for which such a device could demonstrate an advantage over all classical systems. However, these early devices will inevitably remain both noisy and small, precluding the use of quantum error correction. We use high-performance classical tools to construct, optimize, and simulate quantum circuits subject to realistic error models in order to empirically determine the "simulation capacity" of near-term simulation experiments implemented via quantum signal processing (QSP), describing the relationship between simulation time, system size, and resolution of QSP circuits which are optimally configured to balance algorithmic precision and external noise. From simulation capacity models, we estimate maximum tolerable error rate for meaningful simulation experiments on a near-term quantum computer. By exploiting symmetry inherent to the QSP circuit, we further demonstrate that its capacity for quantum simulation can be increased by at least two orders of magnitude if errors are systematic and unitary. We find that a device with $ε^2=10^{-5}$ systematic amplitude errors could meaningfully simulate systems up to $n\approx16$ with an expected failure rate below $10\%$, whereas the largest system a device with a stochastic error rate of $p_ε=10^{-5}$ could meaningfully simulate with the same rate of failure is between $n=3$ and $n=5$ (depending on the stochastic channel). Extrapolating from empirical results, we estimate that one would typically need a stochastic error rate below $p_ε=10^{-8}$ to perform a meaningful $n=50$ simulation experiment with a failure rate below $10\%$, while the same experiment could tolerate systematic unitary errors with strength $ε^2\approx10^{-6}$.

quant-ph↗

arXiv2019

Recurrent Neural Networks in the Eye of Differential Equations

To understand the fundamental trade-offs between training stability, temporal dynamics and architectural complexity of recurrent neural networks~(RNNs), we directly analyze RNN architectures using numerical methods of ordinary differential equations~(ODEs). We define a general family of RNNs--the ODERNNs--by relating the composition rules of RNNs to integration methods of ODEs at discrete time steps. We show that the degree of RNN's functional nonlinearity $n$ and the range of its temporal memory $t$ can be mapped to the corresponding stage of Runge-Kutta recursion and the order of time-derivative of the ODEs. We prove that popular RNN architectures, such as LSTM and URNN, fit into different orders of $n$-$t$-ODERNNs. This exact correspondence between RNN and ODE helps us to establish the sufficient conditions for RNN training stability and facilitates more flexible top-down designs of new RNN architectures using large varieties of toolboxes from numerical integration of ODEs. We provide such an example: Quantum-inspired Universal computing Neural Network~(QUNN), which reduces the required number of training parameters from polynomial in both data length and temporal memory length to only linear in temporal memory length.

cs.LG↗

arXiv2018

High Performance Quantum Modular Multipliers

We present a novel set of reversible modular multipliers applicable to quantum computing, derived from three classical techniques: 1) traditional integer division, 2) Montgomery residue arithmetic, and 3) Barrett reduction. Each multiplier computes an exact result for all binary input values, while maintaining the asymptotic resource complexity of a single (non-modular) integer multiplier. We additionally conduct an empirical resource analysis of our designs in order to determine the total gate count and circuit depth of each fully constructed circuit, with inputs as large as 2048 bits. Our comparative analysis considers both circuit implementations which allow for arbitrary (controlled) rotation gates, as well as those restricted to a typical fault-tolerant gate set.

quant-ph↗

arXiv2016

Iterative Precision Measurement of Branching Ratios Applied to 5P states in 88Sr+

We report on a method for measuring the branching ratios of dipole transitions of trapped atomic ions by performing nested sequences of population inversions. This scheme is broadly applicable and does not use ultrafast pulsed or narrow linewidth lasers. It is simple to perform and insensitive to experimental variables such as laser and magnetic field noise as well as ion heating. To demonstrate its effectiveness, we make the most accurate measurements thus far of the branching ratios of both 5P1/2 and 5P3/2 states in 88Sr+ with sub-1% uncertainties. We measure 17.175(27) for the branching ratio of 5P1/2-5S1/2, 15.845(71) for 5P3/2-5S1/2, and 0.05609(21) for 5P3/2-4D5/2, ten- fold and thirty-fold improvements in precision for 5P1/2 and 5P3/2 branching ratios respectively over the best previous experimental values.

physics.atom-ph↗

arXiv2015

Preventing and Reversing Vacuum-Induced Optical Losses in High-Finesse Tantalum (V) Oxide Mirror Coatings

We study the vacuum-induced degradation of high-finesse optical cavities with mirror coatings composed of SiO$_2$-Ta$_{2}$O$_{5}$ dielectric stacks, and present methods to protect these coatings and to recover their initial quality factor. For separate coatings with reflectivities centered at 370 nm and 422 nm, a vacuum-induced continuous increase in optical loss occurs if the surface-layer coating is made of Ta$_{2}$O$_{5}$, while it does not occur if it is made of SiO$_2$. The incurred optical loss can be reversed by filling the vacuum chamber with oxygen at atmospheric pressure, and the recovery rate can be strongly accelerated by continuous laser illumination at 422 nm. Both the degradation and the recovery processes depend strongly on temperature. We find that a 1 nm-thick layer of SiO$_2$ passivating the Ta$_{2}$O$_{5}$ surface layer is sufficient to reduce the degradation rate by more than a factor of 10, strongly supporting surface oxygen depletion as the primary degradation mechanism.

physics.optics↗

arXiv2013

Participation And performance In 8.02x Electricity And Magnetism: The First Physics MOOC From MITx

Massive Open Online Courses are an exciting new avenue for instruction and research, yet they are full of unknowns. In the Spring of 2013, MITx released its first introductory physics MOOC through the edX platform, generating a total enrollment of 43,000 students from around the world. We describe the population of participants in terms of their age, gender, level of education, and country of origin, highlighting both the diversity of 8.02x enrollees as well as gender gap and retention. Using three midterm exams and the final as waypoints, we highlight performance by different demographic subpopulations and their retention rates. Our work is generally aimed at making a bridge between available MOOC data and topics associated with the Physics Education Research community.

physics.ed-ph↗

arXiv2013

One-dimensional array of ion chains coupled to an optical cavity

We present a novel hybrid system where an optical cavity is integrated with a microfabricated planar-electrode ion trap. The trap electrodes produce a tunable periodic potential allowing the trapping of up to 50 separate ion chains spaced by 160 $μ$m along the cavity axis. Each chain can contain up to 20 individually addressable Yb\textsuperscript{+} ions coupled to the cavity mode. We demonstrate deterministic distribution of ions between the sites of the electrostatic periodic potential and control of the ion-cavity coupling. The measured strength of this coupling should allow access to the strong collective coupling regime with $\lesssim$10 ions. The optical cavity could serve as a quantum information bus between ions or be used to generate a strong wavelength-scale periodic optical potential.

quant-ph↗

arXiv2010

Graph Concatenation for Quantum Codes

Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good quantum codes of relatively large block length, concatenated quantum codes and their generalizations play an important role. We develop a systematic method for constructing concatenated quantum codes based on "graph concatenation", where graphs representing the inner and outer codes are concatenated via a simple graph operation called "generalized local complementation." Our method applies to both binary and non-binary concatenated quantum codes as well as their generalizations.

quant-ph↗

arXiv2007

Bright Source of Cold Ions for Surface-Electrode Traps

We produce large numbers of low-energy ions by photoionization of laser-cooled atoms inside a surface-electrode-based Paul trap. The isotope-selective trap loading rate of $4\times10^{5}$ Yb$^{+}$ ions/s exceeds that attained by photoionization (electron impact ionization) of an atomic beam by four (six) orders of magnitude. Traps as shallow as 0.13 eV are easily loaded with this technique. The ions are confined in the same spatial region as the laser-cooled atoms, which will allow the experimental investigation of interactions between cold ions and cold atoms or Bose-Einstein condensates.

physics.atom-ph↗

arXiv2005

Arbitrarily accurate composite pulses

Systematic errors in quantum operations can be the dominating source of imperfection in achieving control over quantum systems. This problem, which has been well studied in nuclear magnetic resonance, can be addressed by replacing single operations with composite sequences of pulsed operations, which cause errors to cancel by symmetry. Remarkably, this can be achieved without knowledge of the amount of error epsilon. Independent of the initial state of the system, current techniques allow the error to be reduced to O(epsilon^3). Here, we extend the composite pulse technique to cancel errors to O(epsilon^n), for arbitrary n.

quant-ph↗

arXiv2004

NMR Quantum Information Processing

Nuclear Magnetic Resonance (NMR) has provided a valuable experimental testbed for quantum information processing (QIP). Here, we briefly review the use of nuclear spins as qubits, and discuss the current status of NMR-QIP. Advances in the techniques available for control are described along with the various implementations of quantum algorithms and quantum simulations that have been performed using NMR. The recent application of NMR control techniques to other quantum computing systems are reviewed before concluding with a description of the efforts currently underway to transition to solid state NMR systems that hold promise for scalable architectures.

quant-ph↗

arXiv2004

Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms

The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations. We present efficient (size poly(n,d,log(1/ε)) for accuracy ε) quantum circuits for the Schur transform, which is the change of basis between the computational and the Schur bases. These circuits are based on efficient circuits for the Clebsch-Gordan transformation. We also present an efficient circuit for a limited version of the Schur transform in which one needs only to project onto different Schur subspaces. This second circuit is based on a generalization of phase estimation to any nonabelian finite group for which there exists a fast quantum Fourier transform.

quant-ph↗

arXiv2003

Experimental implementation of an adiabatic quantum optimization algorithm

We report the realization of a nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic quantum algorithms offer new insight into how quantum resources can be used to solve hard problems. This experiment uses a particularly well suited three quantum bit molecule and was made possible by introducing a technique that encodes general instances of the given optimization problem into an easily applicable Hamiltonian. Our results indicate an optimal run time of the adiabatic algorithm that agrees well with the prediction of a simple decoherence model.

quant-ph↗

arXiv2001

Quantum Digital Signatures

We present a quantum digital signature scheme whose security is based on fundamental principles of quantum physics. It allows a sender (Alice) to sign a message in such a way that the signature can be validated by a number of different people, and all will agree either that the message came from Alice or that it has been tampered with. To accomplish this task, each recipient of the message must have a copy of Alice's "public key," which is a set of quantum states whose exact identity is known only to Alice. Quantum public keys are more difficult to deal with than classical public keys: for instance, only a limited number of copies can be in circulation, or the scheme becomes insecure. However, in exchange for this price, we achieve unconditionally secure digital signatures. Sending an m-bit message uses up O(m) quantum bits for each recipient of the public key. We briefly discuss how to securely distribute quantum public keys, and show the signature scheme is absolutely secure using one method of key distribution. The protocol provides a model for importing the ideas of classical public key cryptography into the quantum world.

quant-ph↗

arXiv2000

Quantum algorithm for distributed clock synchronization

The clock synchronization problem is to determine the time difference $Δ$ between two spatially separated clocks. When message delivery times between the two clocks are uncertain, $O(2^{2n})$ classical messages must be exchanged between the clocks to determine $n$ digits of $Δ$. On the other hand, as we show, there exists a quantum algorithm to obtain $n$ digits of $Δ$ while communicating only O(n) quantum messages.

quant-ph↗