arXiv subjects

Frank K. Wilhelm

Publications and source records attributed to Frank K. Wilhelm.

At least 73 records · Page 4Linked to original sources

arXiv2018

Environmental effects in quantum annealing

For quantum annealing, as opposed to circuit based quantum computing, the solution to a computational problem is encoded in the ground state of a quantum system. Therefore its susceptibility to environmental effects is a different but not less important open question essential to a scalable implementation. In this work we use renormalization group techniques to study the effect of Ohmic baths in a regime typical for practical adiabatic quantum computation. We show qualitative change to the effective Hamiltonian as well as the reduced qubit density matrix encoding entanglement between system and bath. An effective dephasing of the reduced density matrix limits the extractable information from many qubit entangled groundstates. We find that the annealing process is no longer restricted to the qubits and discuss possible drawbacks or benefits of annealing in the combined system--bath states.

quant-ph↗

arXiv2018

Optimized cross-resonance gate for coupled transmon systems

The cross-resonant gate is an entangling gate for fixed frequency superconducting qubits introduced for untunable qubits. While being simple and extensible, it suffers from long duration and limited fidelity. Using two different optimal control algorithms, we probe the quantum speed limit for a CNOT gate in this system. We show that the ability to approach this limit depends strongly on the ansatz used to describe the optimal control pulse. A piecewise constant ansatz with a single carrier leads to an experimentally feasible pulse shape, shorter than the one currently used in experiments, but that remains relatively far from the speed limit. On the other hand, an ansatz based on the two dominant frequencies involved in the optimal control problem allows to generate an optimal solution more than twice as fast, in under $30$ns. This comes close to the theoretical quantum speed limit, which we estimate at $15$ns for typical circuit-QED parameters, which is more than an order of magnitude faster than current experimental microwave-driven realizations, and more than twice as fast as tunable direct-coupling experimental realizations.

quant-ph↗

arXiv2018

Gradient optimization of analytic controls: the route to high accuracy quantum optimal control

Quantum computation places very stringent demands on gate fidelities, and experimental implementations require both the controls and the resultant dynamics to conform to hardware-specific constraints. Superconducting qubits present the additional requirement that pulses must have simple parameterizations, so they can be further calibrated in the experiment, to compensate for uncertainties in system parameters. Other quantum technologies, such as sensing, require extremely high fidelities. We present a novel, conceptually simple and easy-to-implement gradient-based optimal control technique named Gradient Optimization of Analytic conTrols (GOAT), which satisfies all the above requirements, unlike previous approaches. To demonstrate GOAT's capabilities, with emphasis on flexibility and ease of subsequent calibration, we optimize fast coherence-limited pulses for two leading superconducting qubits architectures - flux-tunable transmons and fixed-frequency transmons with tunable couplers.

quant-ph↗

arXiv2018

Nonlinear Parity Readout with a Microwave Photodetector

Robust high-fidelity parity measurment is an important operation in many applications of quantum computing. In this work we show how in a circuit-QED architecture, one can measure parity in a single shot at very high contrast by taking advantage of the nonlinear behavior of a strongly driven microwave cavity coupled to one or multiple qubits. We work in a nonlinear dispersive regime treated in an exact dispersive transformation. We show that appropriate tuning of experimental parameters leads to very high contrast in the cavity and therefore to a high efficiency parity readout with a microwave photon counter or another amplitude detector. These tuning conditions are based on nonlinearity and are hence more robust than previously described linear tuning schemes. In the first part of the paper we show in detail how to achieve this for two qubit parity measurements and extend this to $N$ qubits in the second part of the paper. We also study the QNDness of the protocol.

quant-ph↗

arXiv2017

The European Quantum Technologies Roadmap

Within the last two decades, Quantum Technologies (QT) have made tremendous progress, moving from Noble Prize award-winning experiments on quantum physics into a cross-disciplinary field of applied research. Technologies are being developed now that explicitly address individual quantum states and make use of the 'strange' quantum properties, such as superposition and entanglement. The field comprises four domains: Quantum Communication, Quantum Simulation, Quantum Computation, and Quantum Sensing and Metrology. One success factor for the rapid advancement of QT is a well-aligned global research community with a common understanding of the challenges and goals. In Europe, this community has profited from several coordination projects, which have orchestrated the creation of a 150-page QT Roadmap. This article presents an updated summary of this roadmap. Besides sections on the four domains of QT, we have included sections on Quantum Theory and Software, and on Quantum Control, as both are important areas of research that cut across all four domains. Each section, after a short introduction to the domain, gives an overview on its current status and main challenges and then describes the advances in science and technology foreseen for the next ten years and beyond.

quant-ph↗

arXiv2017

Benchmarking non-simulable quantum processes via symmetry conservation

As quantum devices scale up, many-body quantum gates and algorithms begin to surpass what is possible to simulate classically. Validation methods which rely on such classical simulation, such as process tomography and randomized benchmarking, cannot efficiently check correctness of most of the processes involved. In particular non-Clifford gates are a requirement for not only universal quantum computation but for any algorithm or quantum simulation that yields fundamental speedup in comparison with its classical counterpart. We show that it is in fact still possible to validate such non-simulable processes by taking advantage of expected or engineered conservations laws in the system, combined with a unitary one-design strategy to randomize errors over the computational Hilbert space. We show that in the context of (fault-tolerant) quantum error correction, we can construct a one-design using the logically encoded Clifford group over the engineered error-free stabilizer subspace to obtain average error for arbitrary logically-encoded gates and algorithms. In the case of benchmarking simulation of physical systems, these can have various exotic symmetries over which one-design strategies can nonetheless be constructed. We give examples for fermionic systems which conserve particle number, as well as for the Fermi-Hubbard model. The symmetry benchmarking method preserves robustness to state preparation and measurement imperfections.

quant-ph↗

arXiv2017

Implementation of the iFREDKIN gate in scalable superconducting architecture for the quantum simulation of Fermionic systems

We present a Superconducting Planar ARchitecture for Quantum Simulations (SPARQS) intended to implement a scalable qubit layout for quantum simulators. To this end, we describe the iFREDKIN gate as a controlled entangler for the simulation of Fermionic systems that is advantageous if it can be directly implemented. Using optimal control, we show that and how this gate can be efficiently implemented in the SPARQS circuit, making it a promising platform and control scheme for quantum simulations. Such a quantum simulator can be built with current quantum technologies to advance the design of molecules and quantum materials.

quant-ph↗

arXiv2016

Simultaneous model selection and parameter estimation: A superconducting qubit coupled to a bath of incoherent two-level systems

In characterization of quantum systems, adapting measurement settings based on data while it is collected can generally outperform in efficiency conventional measurements that are carried out independently of data. The existing methods for choosing measurement settings adaptively assume that the model, or the number of unknown parameters, is known. We introduce simultaneous adaptive model selection and parameter estimation. We apply our technique for characterization of a superconducting qubit and a bath of incoherent two-level systems, a leading decoherence mechanism in the state-of-the-art superconducting qubits.

quant-ph↗

arXiv2016

Optimal Qubit Control Using Single-Flux Quantum Pulses

Single flux quantum pulses are a natural candidate for on-chip control of superconducting qubits. We show that they can drive high-fidelity single-qubit rotations---even in leaky transmon qubits---if the pulse sequence is suitably optimized. We achieve this objective by showing that, for these restricted all-digital pulses, genetic algorithms can be made to converge to arbitrarily low error, verified up to a reduction in gate error by 2 orders of magnitude compared to an evenly spaced pulse train. Timing jitter of the pulses is taken into account, exploring the robustness of our optimized sequence. This approach takes us one step further towards on-chip qubit controls.

quant-ph↗

arXiv2016

Quantum Simulation of a Quantum Stochastic Walk

The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk, which allows for incoherent movement of the walker, and therefore, directionality, is a generalization on the fully coherent quantum walk. While a quantum stochastic walk can always be described in Lindblad formalism, this does not mean that it can be microscopically derived in the standard weak-coupling limit under the Born-Markov approximation. This restricts the class of quantum stochastic walks that can be experimentally realized in a simple manner. To circumvent this restriction, we introduce a technique to simulate open system evolution on a fully coherent quantum computer, using a quantum trajectories style approach. We apply this technique to a broad class of quantum stochastic walks, and show that they can be simulated with minimal experimental resources. Our work opens the path towards the experimental realization of quantum stochastic walks on large graphs with existing quantum technologies.

quant-ph↗

arXiv2016

Hybrid benchmarking of arbitrary quantum gates

We present a protocol for Interleaved Randomized Benchmarking of arbitrary quantum gates using Monte Carlo sampling of quantum states. It is generally applicable, including non-Clifford gates while preserving key advantages of Randomized Benchmarking such as error amplification as well as independence from state preparation and measurement errors. This property is crucial for implementations in many contemporary systems. Although the protocol scales exponentially in the number of qubits, it is superior to direct Monte Carlo sampling of the average gate fidelity in both the total number of experiments by orders of magnitude and savings in classical preprocessing, that are exponential.

quant-ph↗

arXiv2016

Quantum gates and architecture for the quantum simulation of the Fermi-Hubbard model

Quantum computers are the ideal platform for quantum simulations. Given enough coherent operations and qubits, such machines can be leveraged to simulate strongly correlated materials, where intricate quantum effects give rise to counter-intuitive macroscopic phenomena such as high-temperature superconductivity. In this paper, we provide a gate decomposition and an architecture for a quantum simulator used to simulate the Fermi-Hubbard model in a hybrid variational quantum-classical algorithm. We propose a simple planar implementation-independent layout of qubits that can also be used to simulate more general fermionic systems. By working through a concrete application, we show the gate decomposition used to simulate the Hamiltonian of a cluster of the Fermi-Hubbard model. We briefly analyze the Trotter-Suzuki errors and estimate the scaling properties of the algorithm for more complex applications.

quant-ph↗

arXiv2016

On the physical realizability of quantum stochastic walks

Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with that of a classical random walk, through open system evolution of a quantum system. Quantum stochastic walks have been shown to have applications in as far reaching fields as artificial intelligence. However, there are significant constraints on the kind of open system evolutions that can be realized in a physical experiment. In this work, we discuss the restrictions on the allowed open system evolution, and the physical assumptions underpinning them. We show that general implementations would require the complete solution of the underlying unitary dynamics, and sophisticated reservoir engineering, thus weakening the benefits of experimental investigations.

quant-ph↗

arXiv2016

Transient dynamics of a superconducting nonlinear oscillator

We investigate the transient dynamics of a lumped-element oscillator based on a dc superconducting quantum interference device (SQUID). The SQUID is shunted with a capacitor forming a nonlinear oscillator with resonance frequency in the range of several GHz. The resonance frequency is varied by tuning the Josephson inductance of the SQUID with on-chip flux lines. We report measurements of decaying oscillations in the time domain following a brief excitation with a microwave pulse. The nonlinearity of the SQUID oscillator is probed by observing the ringdown response for different excitation amplitudes while the SQUID potential is varied by adjusting the flux bias. Simulations are performed on a model circuit by numerically solving the corresponding Langevin equations incorporating the SQUID potential at the experimental temperature and using parameters obtained from separate measurements characterizing the SQUID oscillator. Simulations are in good agreement with the experimental observations of the ringdowns as a function of applied magnetic flux and pulse amplitude. We observe a crossover between the occurrence of ringdowns close to resonance and adiabatic following at larger detuning from the resonance. We also discuss the occurrence of phase jumps at large amplitude drive. Finally, we briefly outline prospects for a readout scheme for superconducting flux qubits based on the discrimination between ringdown signals for different levels of magnetic flux coupled to the SQUID.

cond-mat.supr-con↗

arXiv2016

Adaptive identification of coherent states

We present methods for efficient characterization of an optical coherent state $|α\rangle$. We choose measurement settings adaptively and stochastically, based on data while it is collected. Our algorithm divides the estimation into two distinct steps: (i) before the first detection of a vacuum state, the probability of choosing a measurement setting is proportional to detecting vacuum with the setting, which makes using too similar measurement settings twice unlikely; and (ii) after the first detection of vacuum, we focus measurements in the region where vacuum is most likely to be detected. In step (i) [(ii)] the detection of vacuum (a photon) has a significantly larger effect on the shape of the posterior probability distribution of $α$. Compared to nonadaptive schemes, our method makes the number of measurement shots required to achieve a certain level of accuracy smaller approximately by a factor proportional to the area describing the initial uncertainty of $α$ in phase space. While this algorithm is not directly robust against readout errors, we make it such by introducing repeated measurements in step (i).

quant-ph↗

arXiv2015

A method to efficiently simulate the thermodynamical properties of the Fermi-Hubbard model on a quantum computer

Many phenomena of strongly correlated materials are encapsulated in the Fermi-Hubbard model whose thermodynamical properties can be computed from its grand canonical potential according to standard procedures. In general, there is no closed form solution for lattices of more than one spatial dimension, but solutions can be approximated with cluster perturbation theory. To model long-range effects such as order parameters, a powerful method to compute the cluster's Green's function consists in finding its self-energy through a variational principle of the grand canonical potential. This opens the possibility of studying various phase transitions at finite temperature in the Fermi-Hubbard model. However, a classical cluster solver quickly hits an exponential wall in the memory (or computation time) required to store the computation variables. Here it is shown theoretically that that the cluster solver can be mapped to a subroutine on a quantum computer whose quantum memory scales as the number of orbitals in the simulated cluster. A quantum computer with a few tens of qubits could therefore simulate the thermodynamical properties of complex fermionic lattices inaccessible to classical supercomputers.

quant-ph↗

arXiv2015

Quantum control of population transfer between vibrational states in an optical lattice

We study quantum control techniques, specifically Adiabatic Rapid Passage (ARP) and Gradient Ascent Pulse Engineering (GRAPE), for transferring atoms trapped in an optical lattice between different vibrational states. We compare them with each other and with previously studied coupling schemes in terms of performance. In our study of ARP, we realize control of the vibrational states by tuning the frequency of a spatial modulation through the inhomogeneously broadened vibrational absorption spectrum. We show that due to the presence of multiple crossings, the population transfer depends on the direction of the frequency sweep, in contrast to traditional ARP. In a second study, we control these states by applying a pulse sequence involving both the displacement of the optical lattice and modulation of the lattice depth. This pulse is engineered via the GRAPE algorithm to maximize the number of atoms transferred from the initial (ground) state to the first excited state. We find that the ARP and the GRAPE techniques are superior to the previously tested techniques at transferring population into the first excited state from the ground state: $38.9\pm0.2\%$ and $39\pm2\%$ respectively. GRAPE outperforms ARP in leaving the higher excited states unpopulated (less than $3.3\%$ of the ground state population, at $84\%$ confidence level), while $18.7\pm0.3\%$ of the ground state population is transferred into higher excited states by using ARP. On the other hand, ARP creates a normalized population inversion of $0.21\pm0.02$, which is the highest obtained by any of the control techniques we have investigated.

quant-ph↗

arXiv2015

Characterization of decohering quantum systems: Machine learning approach

Adaptive data collection and analysis, where data are being fed back to update the measurement settings, can greatly increase speed, precision, and reliability of the characterization of quantum systems. However, decoherence tends to make adaptive characterization difficult. As an example, we consider two coupled discrete quantum systems. When one of the systems can be controlled and measured, the standard method to characterize another, with an unknown frequency $ω_{\rm r}$, is swap spectroscopy. Here, adapting measurements can provide estimates whose error decreases exponentially in the number of measurement shots rather than as a power law in conventional swap spectroscopy. However, when the decoherence time is so short that an excitation oscillating between the two systems can only undergo less than a few tens of vacuum Rabi oscillations, this approach can be marred by a severe limit on accuracy unless carefully designed. We adopt machine learning techniques to search for efficient policies for the characterization of decohering quantum systems. We find, for instance, that when the system undergoes more than 2 Rabi oscillations during its relaxation time $T_1$, $O(10^3)$ measurement shots are sufficient to reduce the squared error of the Bayesian initial prior of the unknown frequency $ω_{\rm r}$ by a factor $O(10^4)$ or larger. We also develop policies optimized for extreme initial parameter uncertainty and for the presence of imperfections in the readout.

quant-ph↗