arXiv subjects

Erik Nielsen

Publications and source records attributed to Erik Nielsen.

At least 37 records · Page 2Linked to original sources

arXiv2020

Wildcard error: Quantifying unmodeled errors in quantum processors

Error models for quantum computing processors describe their deviation from ideal behavior and predict the consequences in applications. But those processors' experimental behavior -- the observed outcome statistics of quantum circuits -- are rarely consistent with error models, even in characterization experiments like randomized benchmarking (RB) or gate set tomography (GST), where the error model was specifically extracted from the data in question. We show how to resolve these inconsistencies, and quantify the rate of unmodeled errors, by augmenting error models with a parameterized wildcard error model. Adding wildcard error to an error model relaxes and weakens its predictions in a controlled way. The amount of wildcard error required to restore consistency with data quantifies how much unmodeled error was observed, in a way that facilitates direct comparison to standard gate error rates. Using both simulated and experimental data, we show how to use wildcard error to reconcile error models derived from RB and GST experiments with inconsistent data, to capture non-Markovianity, and to quantify all of a processor's observed error.

quant-ph↗

arXiv2020

Detecting and tracking drift in quantum information processors

If quantum information processors are to fulfill their potential, the diverse errors that affect them must be understood and suppressed. But errors typically fluctuate over time, and the most widely used tools for characterizing them assume static error modes and rates. This mismatch can cause unheralded failures, misidentified error modes, and wasted experimental effort. Here, we demonstrate a spectral analysis technique for resolving time dependence in quantum processors. Our method is fast, simple, and statistically sound. It can be applied to time-series data from any quantum processor experiment. We use data from simulations and trapped-ion qubit experiments to show how our method can resolve time dependence when applied to popular characterization protocols, including randomized benchmarking, gate set tomography, and Ramsey spectroscopy. In the experiments, we detect instability and localize its source, implement drift control techniques to compensate for this instability, and then demonstrate that the instability has been suppressed.

quant-ph↗

arXiv2020

Detecting crosstalk errors in quantum information processors

Crosstalk occurs in most quantum computing systems with more than one qubit. It can cause a variety of correlated and nonlocal crosstalk errors that can be especially harmful to fault-tolerant quantum error correction, which generally relies on errors being local and relatively predictable. Mitigating crosstalk errors requires understanding, modeling, and detecting them. In this paper, we introduce a comprehensive framework for crosstalk errors and a protocol for detecting and localizing them. We give a rigorous definition of crosstalk errors that captures a wide range of disparate physical phenomena that have been called "crosstalk", and a concrete model for crosstalk-free quantum processors. Errors that violate this model are crosstalk errors. Next, we give an equivalent but purely operational (model-independent) definition of crosstalk errors. Using this definition, we construct a protocol for detecting a large class of crosstalk errors in a multi-qubit processor by finding conditional dependencies between observed experimental probabilities. It is highly efficient, in the sense that the number of unique experiments required scales at most cubically, and very often quadratically, with the number of qubits. We demonstrate the protocol using simulations of 2-qubit and 6-qubit processors.

quant-ph↗

arXiv2020

Probing quantum processor performance with pyGSTi

PyGSTi is a Python software package for assessing and characterizing the performance of quantum computing processors. It can be used as a standalone application, or as a library, to perform a wide variety of quantum characterization, verification, and validation (QCVV) protocols on as-built quantum processors. We outline pyGSTi's structure, and what it can do, using multiple examples. We cover its main characterization protocols with end-to-end implementations. These include gate set tomography, randomized benchmarking on one or many qubits, and several specialized techniques. We also discuss and demonstrate how power users can customize pyGSTi and leverage its components to create specialized QCVV protocols and solve user-specific problems.

quant-ph↗

arXiv2019

Direct randomized benchmarking for multi-qubit devices

Benchmarking methods that can be adapted to multi-qubit systems are essential for assessing the overall or "holistic" performance of nascent quantum processors. The current industry standard is Clifford randomized benchmarking (RB), which measures a single error rate that quantifies overall performance. But scaling Clifford RB to many qubits is surprisingly hard. It has only been performed on 1, 2, and 3 qubits as of this writing. This reflects a fundamental inefficiency in Clifford RB: the $n$-qubit Clifford gates at its core have to be compiled into large circuits over the 1- and 2-qubit gates native to a device. As $n$ grows, the quality of these Clifford gates quickly degrades, making Clifford RB impractical at relatively low $n$. In this Letter, we propose a direct RB protocol that mostly avoids compiling. Instead, it uses random circuits over the native gates in a device, seeded by an initial layer of Clifford-like randomization. We demonstrate this protocol experimentally on 2 -- 5 qubits, using the publicly available IBMQX5. We believe this to be the greatest number of qubits holistically benchmarked, and this was achieved on a freely available device without any special tuning up. Our protocol retains the simplicity and convenient properties of Clifford RB: it estimates an error rate from an exponential decay. But it can be extended to processors with more qubits -- we present simulations on 10+ qubits -- and it reports a more directly informative and flexible error rate than the one reported by Clifford RB. We show how to use this flexibility to measure separate error rates for distinct sets of gates, which includes tasks such as measuring an average CNOT error rate.

quant-ph↗

arXiv2017

Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography

Quantum information processors promise fast algorithms for problems inaccessible to classical computers. But since qubits are noisy and error-prone, they will depend on fault-tolerant quantum error correction (FTQEC) to compute reliably. Quantum error correction can protect against general noise if -- and only if -- the error in each physical qubit operation is smaller than a certain threshold. The threshold for general errors is quantified by their diamond norm. Until now, qubits have been assessed primarily by randomized benchmarking, which reports a different "error rate" that is not sensitive to all errors, and cannot be compared directly to diamond norm thresholds. Here we use gate set tomography (GST) to completely characterize operations on a trapped-Yb$^+$-ion qubit and demonstrate with very high ($>95\%$) confidence that they satisfy a rigorous threshold for FTQEC (diamond norm $\leq6.7\times10^{-4}$).

quant-ph↗

arXiv2016

Valley splitting of single-electron Si MOS quantum dots

Silicon-based metal-oxide-semiconductor quantum dots are prominent candidates for high-fidelity, manufacturable qubits. Due to silicon's band structure, additional low-energy states persist in these devices, presenting both challenges and opportunities. Although the physics governing these valley states has been the subject of intense study, quantitative agreement between experiment and theory remains elusive. Here, we present data from a new experiment probing the valley states of quantum dot devices and develop a theory that is in quantitative agreement with both the new experiment and a recently reported one. Through sampling millions of realistic cases of interface roughness, our method provides evidence that, despite radically different processing, the valley physics between the two samples is essentially the same. This work provides the first evidence that valley splitting can be deterministically predicted and controlled in metal oxide semiconductor quantum dots, a critical requirement for such systems to realize a reliable qubit platform.

cond-mat.mes-hall↗

arXiv2016

Optimization of a solid-state electron spin qubit using Gate Set Tomography

State of the art qubit systems are reaching the gate fidelities required for scalable quantum computation architectures. Further improvements in the fidelity of quantum gates demands characterization and benchmarking protocols that are efficient, reliable and extremely accurate. Ideally, a benchmarking protocol should also provide information on how to rectify residual errors. Gate Set Tomography (GST) is one such protocol designed to give detailed characterization of as-built qubits. We implemented GST on a high-fidelity electron-spin qubit confined by a single $^{31}$P atom in $^{28}$Si. The results reveal systematic errors that a randomized benchmarking analysis could measure but not identify, whereas GST indicated the need for improved calibration of the length of the control pulses. After introducing this modification, we measured a new benchmark average gate fidelity of $99.942(8)\%$, an improvement on the previous value of $99.90(2)\%$. Furthermore, GST revealed high levels of non-Markovian noise in the system, which will need to be understood and addressed when the qubit is used within a fault-tolerant quantum computation scheme.

cond-mat.mes-hall↗

arXiv2015

Multivalley effective mass theory simulation of donors in silicon

Last year, Salfi et al. made the first direct measurements of a donor wave function and found extremely good theoretical agreement with atomistic tight-binding [Salfi et al., Nat. Mater. 13, 605 (2014)]. Here, we show that multi-valley effective mass theory, applied properly, does achieve close agreement with tight-binding and hence gives reliable predictions. To demonstrate this, we variationally solve the coupled six-valley Shindo-Nara equations, including silicon's full Bloch functions. Surprisingly, we find that including the full Bloch functions necessitates a tetrahedral, rather than spherical, donor central cell correction to accurately reproduce the experimental energy spectrum of a phosphorus impurity in silicon. We cross-validate this method against atomistic tight-binding calculations, showing that the two theories agree well for the calculation of donor-donor tunnel coupling. Further, we benchmark our results by performing a statistical uncertainty analysis, confirming that derived quantities such as the wave function profile and tunnel couplings are robust with respect to variational energy fluctuations. Finally, we apply this method to exhaustively enumerate the tunnel coupling for all donor-donor configurations within a large search volume, demonstrating conclusively that the tunnel coupling has no spatially stable regions. Though this instability is problematic for reliably coupling donor pairs for two-qubit operations, we identify specific target locations where donor qubits can be placed with scanning tunneling microscopy technology to achieve reliably large tunnel couplings.

cond-mat.mes-hall↗

arXiv2015

Transport through an impurity tunnel coupled to a Si/SiGe quantum dot

Achieving controllable coupling of dopants in silicon is crucial for operating donor-based qubit devices, but it is difficult because of the small size of donor-bound electron wavefunctions. Here we report the characterization of a quantum dot coupled to a localized electronic state, and we present evidence of controllable coupling between the quantum dot and the localized state. A set of measurements of transport through this device enable the determination of the most likely location of the localized state, consistent with an electronically active impurity in the quantum well near the edge of the quantum dot. The experiments we report are consistent with a gate-voltage controllable tunnel coupling, which is an important building block for hybrid donor and gate-defined quantum dot devices.

cond-mat.mes-hall↗

arXiv2014

Microwave-driven coherent operations of a semiconductor quantum dot charge qubit

A most intuitive realization of a qubit is a single electron charge sitting at two well-defined positions, such as the left and right sides of a double quantum dot. This qubit is not just simple but also has the potential for high-speed operation, because of the strong coupling of electric fields to the electron. However, charge noise also couples strongly to this qubit, resulting in rapid dephasing at nearly all operating points, with the exception of one special 'sweet spot'. Fast dc voltage pulses have been used to manipulate semiconductor charge qubits, but these previous experiments did not achieve high-fidelity control, because dc gating requires excursions away from the sweet spot. Here, by using resonant ac microwave driving, we achieve coherent manipulation of a semiconductor charge qubit, demonstrating a Rabi frequency of up to 2GHz, a value approaching the intrinsic qubit frequency of 4.5GHz. Z-axis rotations of the qubit are well-protected at the sweet spot, and by using ac gating, we demonstrate the same protection for rotations about arbitrary axes in the X-Y plane of the qubit Bloch sphere. We characterize operations on the qubit using two independent tomographic approaches: standard process tomography and a newly developed method known as gate set tomography. Both approaches show that this qubit can be operated with process fidelities greater than 86% with respect to a universal set of unitary single-qubit operations.

cond-mat.mes-hall↗

arXiv2014

QCAD Simulation and Optimization of Semiconductor Quantum Dots

We present the Quantum Computer Aided Design (QCAD) simulator that targets modeling multi-dimensional quantum devices, particularly silicon multi-quantum dots (QDs) developed for quantum bits (qubits). This finite-element simulator has three differentiating features: (i) its core contains nonlinear Poisson, effective mass Schrodinger, and Configuration Interaction solvers that have massively parallel capability for high simulation throughput, and can be run individually or combined self-consistently for 1D/2D/3D quantum devices; (ii) the core solvers show superior convergence even at near-zero-Kelvin temperatures, which is critical for modeling quantum computing devices; and (iii) it interfaces directly with the full-featured optimization engine Dakota. In this work, we describe the capabilities and implementation of the QCAD simulation tool, and show how it can be used to both analyze existing experimental QD devices through capacitance calculations, and aid in the design of few-electron multi-QDs. In particular, we observe that computed capacitances are in rough agreement with experiment, and that quantum confinement increases capacitance when the number of electrons is fixed in a quantum dot. Coupling of QCAD with the optimizer Dakota allows for rapid identification and improvement of device layouts that are likely to exhibit few-electron quantum dot characteristics.

cond-mat.mes-hall↗

arXiv2014

Efficient self-consistent quantum transport simulator for quantum devices

We present a self-consistent one-dimensional (1D) quantum transport simulator based on the Contact Block Reduction (CBR) method, aiming for very fast and robust transport simulation of 1D quantum devices. Applying the general CBR approach to 1D open systems results in a set of very simple equations that are derived and given in detail for the first time. The charge self-consistency of the coupled CBR-Poisson equations is achieved by using the predictor-corrector iteration scheme with the optional Anderson acceleration. In addition, we introduce a new way to convert an equilibrium electrostatic barrier potential calculated from an external simulator to an effective doping profile, which is then used by the CBR-Poisson code for transport simulation of the barrier under non-zero biases. The code has been applied to simulate the quantum transport in a double barrier structure and across a tunnel barrier in a silicon double quantum dot. Extremely fast self-consistent 1D simulations of the differential conductance across a tunnel barrier in the quantum dot show better qualitative agreement with experiment than non-self-consistent simulations.

cond-mat.mes-hall↗

arXiv2014

Spontaneous emission in a silicon charge qubit

The interaction between a qubit and its environment provides a channel for energy relaxation which has an energy-dependent timescale governed by the specific coupling mechanism. We measure the rate of inelastic decay in a Si MOS double quantum dot (DQD) charge qubit through sensing the charge state's response to non-adiabatic driving of its excited state population. The charge distribution is sensed remotely in the weak measurement regime. We extract emission rates down to kHz frequencies by measuring the variation of the non-equilibrium charge occupancy as a function of amplitude and dwell times between non-adiabatic pulses. Our measurement of the energy-dependent relaxation rate provides a fingerprint of the relaxation mechanism, indicating that relaxation rates for this Si MOS DQD are consistent with coupling to deformation acoustic phonons.

quant-ph↗

arXiv2013

Robust, self-consistent, closed-form tomography of quantum logic gates on a trapped ion qubit

We introduce and demonstrate experimentally: (1) a framework called "gate set tomography" (GST) for self-consistently characterizing an entire set of quantum logic gates on a black-box quantum device; (2) an explicit closed-form protocol for linear-inversion gate set tomography (LGST), whose reliability is independent of pathologies such as local maxima of the likelihood; and (3) a simple protocol for objectively scoring the accuracy of a tomographic estimate without reference to target gates, based on how well it predicts a set of testing experiments. We use gate set tomography to characterize a set of Clifford-generating gates on a single trapped-ion qubit, and compare the performance of (i) standard process tomography; (ii) linear gate set tomography; and (iii) maximum likelihood gate set tomography.

quant-ph↗

arXiv2013

Four-component united-atom model of bitumen

We propose a four-component molecular model of bitumen. The model includes realistic chemical constituents and introduces a coarse-graining level that suppresses the highest frequency modes. Molecular dynamics simulations of the model are being carried out using Graphic-Processor-Units based software in time spans in order of microseconds, and this enables the study of slow relaxation processes characterizing bitumen. This paper focuses on the high-temperature dynamics as expressed through the mean-square displacement, the stress autocorrelation function, and rotational relaxation. The diffusivity of the individual molecules changes little as a function of temperature and reveals distinct dynamical time scales as a result of the different constituents in the system. Different time scales are also observed for the rotational relaxation. The stress autocorrelation function features a slow non-exponential decay for all temperatures studied. From the stress autocorrelation function, the shear viscosity and shear modulus are evaluated at the highest temperature, showing a viscous response at frequencies below 100 MHz. The model predictions of viscosity and diffusivities are compared to experimental data, giving reasonable agreement. The model shows that the asphaltene, resin and resinous oil tend to form nano-aggregates. The characteristic dynamical relaxation time of these aggregates is different from the homogeneously distributed parts of the system, leading to strong dynamical heterogeneity.

physics.chem-ph↗

arXiv2013

Six-electron semiconductor double quantum dot qubits

We consider a double-quantum-dot (DQD) qubit which contains six electrons instead of the usual one or two. In this spin qubit, quantum information is encoded in a low-lying singlet-triplet space much as in the case of a two-electron DQD qubit. We find that initialization, manipulation, and read- out can be performed similarly to the two-electron case, and that energy gaps remain large enough that these operations can be performed robustly. We consider DQD potentials with parameters chosen to be representative of current experimental capabilities. Results are obtained using two complementary full configuration interaction methods.

cond-mat.mes-hall↗

arXiv2012

A many-electron tight binding method for the analysis of quantum dot systems

We present a method which computes many-electron energies and eigenfunctions by a full configuration interaction which uses a basis of atomistic tight-binding wave functions. This approach captures electron correlation as well as atomistic effects, and is well suited to solid state quantum dot systems containing few electrons, where valley physics and disorder contribute significantly to device behavior. Results are reported for a two-electron silicon double quantum dot as an example.

cond-mat.mes-hall↗