Showing papers by "Isaac L. Chuang published in 2016"
TL;DR: The realization of a scalable Shor algorithm, as proposed by Kitaev, is presented, which has been realized scalably within an ion-trap quantum computer and returns the correct factors with a confidence level exceeding 99%.
Abstract: Certain algorithms for quantum computers are able to outperform their classical counterparts In 1994, Peter Shor came up with a quantum algorithm that calculates the prime factors of a large number vastly more efficiently than a classical computer For general scalability of such algorithms, hardware, quantum error correction, and the algorithmic realization itself need to be extensible Here we present the realization of a scalable Shor algorithm, as proposed by Kitaev We factor the number 15 by effectively employing and controlling seven qubits and four “cache qubits” and by implementing generalized arithmetic operations, known as modular multipliers This algorithm has been realized scalably within an ion-trap quantum computer and returns the correct factors with a confidence level exceeding 99%
382 citations
TL;DR: In this article, the problem of approximating the time-evolution operator $e^{-i\hat{H}t} to error $epsilon, where the Hamiltonian is the projection of a unitary oracle $\hat{U}$ onto the state $|G\rangle$ created by another unitary ORO, is solved with a query complexity of O(t+log(1/πsilon)$ to both oracles that is optimal with respect to all parameters in both the asymptotic and nonasymptotic regime
Abstract: We present the problem of approximating the time-evolution operator $e^{-i\hat{H}t}$ to error $\epsilon$, where the Hamiltonian $\hat{H}=(\langle G|\otimes\hat{\mathcal{I}})\hat{U}(|G\rangle\otimes\hat{\mathcal{I}})$ is the projection of a unitary oracle $\hat{U}$ onto the state $|G\rangle$ created by another unitary oracle. Our algorithm solves this with a query complexity $\mathcal{O}\big(t+\log({1/\epsilon})\big)$ to both oracles that is optimal with respect to all parameters in both the asymptotic and non-asymptotic regime, and also with low overhead, using at most two additional ancilla qubits. This approach to Hamiltonian simulation subsumes important prior art considering Hamiltonians which are $d$-sparse or a linear combination of unitaries, leading to significant improvements in space and gate complexity, such as a quadratic speed-up for precision simulations. It also motivates useful new instances, such as where $\hat{H}$ is a density matrix. A key technical result is `qubitization', which uses the controlled version of these oracles to embed any $\hat{H}$ in an invariant $\text{SU}(2)$ subspace. A large class of operator functions of $\hat{H}$ can then be computed with optimal query complexity, of which $e^{-i\hat{H}t}$ is a special case.
219 citations
TL;DR: In this paper, it was shown that even 5-and 7-qubit codes can yield universal fault-tolerant computation with relatively low overhead, and that error correction is a fundamental aspect of quantum codes.
Abstract: Error correction is a fundamental aspect of quantum codes. Researchers theoretically show that even 5- and 7-qubit codes can yield universal fault-tolerant computation with relatively low overhead.
72 citations
TL;DR: In this article, classical signal processing techniques are adapted to allow the systematic and efficient design of composite quantum gates for weak signals extraction from quantum systems, which is often a test of quantum control.
Abstract: Extracting weak signals from quantum systems is often a test of quantum control. Classical signal-processing techniques are adapted to allow the systematic and efficient design of composite quantum gates for such tasks.
72 citations
TL;DR: In this article, the authors describe a cheating strategy enabled by the features of massive open online courses (MOOCs) and detectable by virtue of the sophisticated data systems that MOOCs provide.
Abstract: We describe a cheating strategy enabled by the features of massive open online courses (MOOCs) and detectable by virtue of the sophisticated data systems that MOOCs provide. The strategy, Copying Answers using Multiple Existences Online (CAMEO), involves a user who gathers solutions to assessment questions using a "harvester" account and then submits correct answers using a separate "master" account. We use a small-scale experiment to verify CAMEO and estimate a "lower bound" for its prevalence among 1.9 million course participants in 115 MOOCs from two universities. Using conservative thresholds, we estimate CAMEO prevalence at 1237 certificates, accounting for 1.3% of the certificates in the 69 MOOCs with CAMEO users. Among earners of 20 or more certificates, 25% have used the CAMEO strategy. CAMEO users are more likely to be young, male, and international than other MOOC certificate earners. We identify preventive strategies that can decrease CAMEO rates and show evidence of their effectiveness in science courses. We detect a cheating strategy used in Massive Open Online Courses (MOOCs).We call this strategy, "Copying Answers using Multiple Existences Online" (CAMEO).We estimate conservatively that at least 1.3% of certificates were earned by CAMEO.Among earners of 20 or more certificates, 25% have used the CAMEO strategy.CAMEO represents one of many threats to the validity of MOOC certifications.
68 citations
TL;DR: In this paper, the authors present a systematic and efficient methodology for composite gate design of arbitrary length, where phase-controlled primitive gates all rotating by the same spin act on a single spin.
Abstract: The creation of composite quantum gates that implement quantum response functions $\hat{U}(\theta)$ dependent on some parameter of interest $\theta$ is often more of an art than a science. Through inspired design, a sequence of $L$ primitive gates also depending on $\theta$ can engineer a highly nontrivial $\hat{U}(\theta)$ that enables myriad precision metrology, spectroscopy, and control techniques. However, discovering new, useful examples of $\hat{U}(\theta)$ requires great intuition to perceive the possibilities, and often brute-force to find optimal implementations. We present a systematic and efficient methodology for composite gate design of arbitrary length, where phase-controlled primitive gates all rotating by $\theta$ act on a single spin. We fully characterize the realizable family of $\hat{U}(\theta)$, provide an efficient algorithm that decomposes a choice of $\hat{U}(\theta)$ into its shortest sequence of gates, and show how to efficiently choose an achievable $\hat{U}(\theta)$ that for fixed $L$, is an optimal approximation to objective functions on its quadratures. A strong connection is forged with \emph{classical} discrete-time signal processing, allowing us to swiftly construct, as examples, compensated gates with optimal bandwidth that implement arbitrary single spin rotations with sub-wavelength spatial selectivity.
37 citations
Journal Article•
TL;DR: A systematic and efficient methodology for composite gate design of arbitrary length, where phase-controlled primitive gates all rotating by $\theta$ act on a single spin, and is fully characterize the realizable family of $\hat{U}(\theta)$.
Abstract: Extracting weak signals from quantum systems is often a test of quantum control. Classical signal-processing techniques are adapted to allow the systematic and efficient design of composite quantum gates for such tasks.
29 citations
TL;DR: In this article, the authors review the recent efforts to create scalable ion systems incorporating unconventional materials such as graphene and indium tin oxide, integrating devices like optical fibers and mirrors, and exploring alternative ion loading and trapping techniques.
Abstract: Scaling up from prototype systems to dense arrays of ions on chip, or vast networks of ions connected by photonic channels, will require developing entirely new technologies that combine miniaturized ion trapping systems with devices to capture, transmit, and detect light, while refining how ions are confined and controlled. Building a cohesive ion system from such diverse parts involves many challenges, including navigating materials incompatibilities and undesired coupling between elements. Here, we review our recent efforts to create scalable ion systems incorporating unconventional materials such as graphene and indium tin oxide, integrating devices like optical fibers and mirrors, and exploring alternative ion loading and trapping techniques.
20 citations
Journal Article•
TL;DR: Recent efforts to create scalable ion systems incorporating unconventional materials such as graphene and indium tin oxide, integrating devices like optical fibers and mirrors, and exploring alternative ion loading and trapping techniques are reviewed.
Abstract: United States. Intelligence Advanced Research Projects Activity. Multi-Qubit Coherent Operations Program
13 citations
TL;DR: In this paper, the effects of rough surface curvature on electric-field noise were investigated by deriving a rough surface Green's function and evaluating its effects on adsorbate-surface binding energies.
Abstract: Electric-field noise is a major source of motional heating in trapped-ion quantum computation. While the influence of trap-electrode geometries on electric-field noise has been studied in patch potential and surface adsorbate models, only smooth surfaces are accounted for by current theory. The effects of roughness, a ubiquitous feature of surface electrodes, are poorly understood. We investigate its impact on electric-field noise by deriving a rough-surface Green's function and evaluating its effects on adsorbate-surface binding energies. At cryogenic temperatures, heating-rate contributions from adsorbates are predicted to exhibit an exponential sensitivity to local surface curvature, leading to either a large net enhancement or suppression over smooth surfaces. For typical experimental parameters, orders-of-magnitude variations in total heating rates can occur depending on the spatial distribution of adsorbates. Through careful engineering of electrode surface profiles, our results suggests that heating rates can be tuned over orders of magnitudes.
10 citations
TL;DR: In this paper, the branching ratio of dipole transitions of trapped atomic ions was measured by performing nested sequences of population inversions, and the results were improved to 17.175(27), 15.845(71), and 0.05609(21) for 5P3/2-4D5/2.
Abstract: 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.
Journal Article•
TL;DR: In this paper, the effects of rough surface curvature on electric-field noise were investigated by deriving a rough surface Green's function and evaluating its effects on adsorbate-surface binding energies.
Abstract: Electric-field noise is a major source of motional heating in trapped-ion quantum computation. While the influence of trap-electrode geometries on electric-field noise has been studied in patch potential and surface adsorbate models, only smooth surfaces are accounted for by current theory. The effects of roughness, a ubiquitous feature of surface electrodes, are poorly understood. We investigate its impact on electric-field noise by deriving a rough-surface Green's function and evaluating its effects on adsorbate-surface binding energies. At cryogenic temperatures, heating-rate contributions from adsorbates are predicted to exhibit an exponential sensitivity to local surface curvature, leading to either a large net enhancement or suppression over smooth surfaces. For typical experimental parameters, orders-of-magnitude variations in total heating rates can occur depending on the spatial distribution of adsorbates. Through careful engineering of electrode surface profiles, our results suggests that heating rates can be tuned over orders of magnitudes.
TL;DR: In this article, the branching ratios of dipole transitions of trapped atomic ions were measured by performing nested sequences of population inversions. But the branching ratio was not used to find the branching of any state to lowest states.
Abstract: We report and demonstrate 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 to species with metastable lambda systems and can be generalized to find the branching of any state to lowest states. It does not use ultrafast pulsed or narrow linewidth lasers and is 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 and states in 88Sr+ with sub-1% uncertainties. We measure 17.175(27) for the – branching ratio, 15.845(71) for –, and 0.056 09(21) for –. These values represent the first precision measurement for –, as well as ten- and thirty-fold improvements in precision respectively for – and – over the best previous experimental values.
Posted Content•
TL;DR: It is shown how the limits of non-transversality can be overcome by performing rounds of intermediate error-correction to create logical gates on stabilizer codes that use no ancillas other than those required for syndrome measurement.
Abstract: It is an oft cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions including magic state distillation. Widely overlooked, however, is the possibility of non-transversal, yet still fault-tolerant, gates that work directly on small quantum codes. Here we demonstrate precisely the existence of such gates. In particular, we show how the limits of non-transversality can be overcome by performing rounds of intermediate error-correction to create logical gates on stabilizer codes that use no ancillas other than those required for syndrome measurement. Moreover, the logical gates we construct, the most prominent examples being Toffoli and controlled-controlled-Z, often complete universal gate sets on their codes. We detail such universal constructions for the smallest quantum codes, the 5-qubit and 7-qubit codes, and then proceed to generalize the approach. One remarkable result of this generalization is that any nondegenerate stabilizer code with a complete set of fault-tolerant single-qubit Clifford gates has a universal set of fault-tolerant gates. Another is the interaction of logical qubits across different stabilizer codes, which, for instance, implies a broadly applicable method of code switching.
Posted Content•
TL;DR: A systematic and efficient methodology for composite gate design of arbitrary length, where phase-controlled primitive gates all rotating by $\theta$ act on a single spin is presented.
Abstract: The creation of composite quantum gates that implement quantum response functions $\hat{U}(\theta)$ dependent on some parameter of interest $\theta$ has historically been more of an art than a science. Through inspired design, a sequence of $L$ primitive gates also depending on $\theta$ can engineer a highly nontrivial $\hat{U}(\theta)$ that enables myriad precision metrology, spectroscopy, and control techniques. However, discovering new useful examples of $\hat{U}(\theta)$ requires great intuition to perceive the possibilities, and often brute-force to find optimal implementations. These demands hobble our imagination of new applications. We present a systematic and efficient methodology for composite gate design of arbitrary length, where phase-controlled primitive gates all rotating by $\theta$ act on a single spin. We fully characterize the realizable family of $\hat{U}(\theta)$, provide an efficient algorithm that decomposes a choice of $\hat{U}(\theta)$ into its shortest sequence of gates, and show how to efficiently choose achievable $\hat{U}(\theta)$ that for fixed $L$, are optimal approximations to objective functions on its quadratures. A strong connection is forged with \emph{classical} discrete-time signal processing, allowing us to swiftly construct, as examples, compensated gates with optimal bandwidth that implement arbitrary single spin rotations with optimal sub-wavelength spatial selectivity.
Journal Article•
TL;DR: In this paper, it was shown that any non-transversal stabilizer code with a complete set of fault-tolerant single-qubit Clifford gates has a universal set of logical gates.
Abstract: It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions including magic state distillation. Widely overlooked, however, is the possibility of non-transversal, yet still fault-tolerant, gates that work directly on small quantum codes. Here we demonstrate precisely the existence of such gates. In particular, we show how the limits of non-transversality can be overcome by performing rounds of intermediate error-correction to create logical gates on stabilizer codes that use no ancillas other than those required for syndrome measurement. Moreover, the logical gates we construct, the most prominent examples being Toffoli and controlled-controlled-Z, often complete universal gate sets on their codes. We detail such universal constructions for the smallest quantum codes, the 5-qubit and 7-qubit codes, and then proceed to generalize the approach. One remarkable result of this generalization is that any nondegenerate stabilizer code with a complete set of fault-tolerant single-qubit Clifford gates has a universal set of fault-tolerant gates. Another is the interaction of logical qubits across different stabilizer codes, which, for instance, implies a broadly applicable method of code switching.
TL;DR: It is shown how the limits of non-transversality can be overcome by performing rounds of intermediate error-correction to create logical gates on stabilizer codes that use no ancillas other than those required for syndrome measurement.
Abstract: It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions including magic state distillation. Widely overlooked, however, is the possibility of non-transversal, yet still fault-tolerant, gates that work directly on small quantum codes. Here we demonstrate precisely the existence of such gates. In particular, we show how the limits of non-transversality can be overcome by performing rounds of intermediate error-correction to create logical gates on stabilizer codes that use no ancillas other than those required for syndrome measurement. Moreover, the logical gates we construct, the most prominent examples being Toffoli and controlled-controlled-Z, often complete universal gate sets on their codes. We detail such universal constructions for the smallest quantum codes, the 5-qubit and 7-qubit codes, and then proceed to generalize the approach. One remarkable result of this generalization is that any nondegenerate stabilizer code with a complete set of fault-tolerant single-qubit Clifford gates has a universal set of fault-tolerant gates. Another is the interaction of logical qubits across different stabilizer codes, which, for instance, implies a broadly applicable method of code switching.