# Erik NielsenSandia National Laboratories

Erik Nielsen

## About

65

Publications

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1,213

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## Publications

Publications (65)

Randomized benchmarking (RB) protocols are the most widely used methods for assessing the performance of quantum gates. However, the existing RB methods either do not scale to many qubits or cannot benchmark a universal gate set. Here, we introduce and demonstrate a technique for scalable RB of many universal and continuously parameterized gate set...

Errors in quantum logic gates are usually modeled by quantum process matrices (CPTP maps). But process matrices can be opaque and unwieldy. We show how to transform the process matrix of a gate into an error generator that represents the same information more usefully. We construct a basis of simple and physically intuitive elementary error generat...

Real-world quantum computers have grown sufficiently complex that they can no longer be simulated by classical supercomputers, but their computational power remains limited by errors. These errors corrupt the results of quantum algorithms, and it is no longer always feasible to use classical simulations to directly check the correctness of quantum...

Measurements that occur within the internal layers of a quantum circuit—midcircuit measurements—are a useful quantum-computing primitive, most notably for quantum error correction. Midcircuit measurements have both classical and quantum outputs, so they can be subject to error modes that do not exist for measurements that terminate quantum circuits...

Quantum computers can now run interesting programs, but each processor’s capability—the set of programs that it can run successfully—is limited by hardware errors. These errors can be complicated, making it difficult to accurately predict a processor’s capability. Benchmarks can be used to measure capability directly, but current benchmarks have li...

The performance of quantum gates is often assessed using some form of randomized benchmarking. However, the existing methods become infeasible for more than approximately five qubits. Here we show how to use a simple and customizable class of circuits -- randomized mirror circuits -- to perform scalable, robust, and flexible randomized benchmarking...

Crosstalk is a leading source of failure in multiqubit quantum information processors. It can arise from a wide range of disparate physical phenomena, and can introduce subtle correlations in the errors experienced by a device. Several hardware characterization protocols are able to detect the presence of crosstalk, but few provide sufficient infor...

Gate set tomography (GST) is a protocol for detailed, predictive characterization of logic operations (gates) on quantum computing processors. Early versions of GST emerged around 2012-13, and since then it has been refined, demonstrated, and used in a large number of experiments. This paper presents the foundations of GST in comprehensive detail....

We present a simple and powerful technique for finding a good error model for a quantum processor. The technique iteratively tests a nested sequence of models against data obtained from the processor, and keeps track of the best-fit model and its wildcard error (a metric of the amount of unmodeled error) at each step. Each best-fit model, along wit...

Crosstalk is a leading source of failure in multiqubit quantum information processors. It can arise from a wide range of disparate physical phenomena, and can introduce subtle correlations in the errors experienced by a device. Several hardware characterization protocols are able to detect the presence of crosstalk, but few provide sufficient infor...

Measurements that occur within the internal layers of a quantum circuit -- mid-circuit measurements -- are an important quantum computing primitive, most notably for quantum error correction. Mid-circuit measurements have both classical and quantum outputs, so they can be subject to error modes that do not exist for measurements that terminate quan...

We present a simple and powerful technique for finding a good error model for a quantum processor. The technique iteratively tests a nested sequence of models against data obtained from the processor, and keeps track of the best-fit model and its wildcard error (a quantification of the unmodeled error) at each step. Each best-fit model, along with...

Errors in quantum logic gates are usually modeled by quantum process matrices (CPTP maps). But process matrices can be opaque, and unwieldy. We show how to transform a gate's process matrix into an error generator that represents the same information more usefully. We construct a basis of simple and physically intuitive elementary error generators,...

This paper describes our work over the past few years to use tools from quantum chemistry to describe electronic structure of nanoelectronic devices. These devices, dubbed “artificial atoms,” comprise a few electrons, confined by semiconductor heterostructures, impurities, and patterned electrodes, and are of intense interest due to potential appli...

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)...

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 was...

Gate set tomography (GST) is a protocol for detailed, predictive characterization of logic operations (gates) on quantum computing processors. Early versions of GST emerged around 2012-13, and since then it has been refined, demonstrated, and used in a large number of experiments. This paper presents the foundations of GST in comprehensive detail....

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, modeli...

A quantum computer has now solved a specialized problem believed to be intractable for supercomputers, suggesting that quantum processors may soon outperform supercomputers on scientifically important problems. But flaws in each quantum processor limit its capability by causing errors in quantum programs, and it is currently difficult to predict wh...

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 wha...

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 wha...

Crosstalk occurs in most quantum computing systems with more than one qubit. It can cause a variety of correlated and nonlocal errors, which we call crosstalk errors. They can be especially harmful to fault-tolerant quantum error correction, which generally relies on errors being local and relatively predictable. Mitigating crosstalk errors require...

If quantum information processors (QIPs) are ever to fulfill their potential, the diverse errors that impact them must be understood and suppressed. But errors fluctuate over time in most processors and the most widely used tools for characterizing them assume static error modes and rates. This mismatch can cause unheralded failures, misidentified...

Benchmarking methods that can be adapted to multiqubit 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 sur...

Benchmarking methods that can be adapted to multi-qubit systems are essential tools 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...

This corrects the article DOI: 10.1038/ncomms14485.

Despite their ubiquity in nanoscale electronic devices, the physics of tunnel barriers has not been developed to the extent necessary for the engineering of devices in the few-electron regime. This problem is of urgent interest, as this is the precise regime into which current, extreme-scale electronics fall. Here, we propose theoretically and vali...

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 opera...

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, quanti...

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, quanti...

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 ho...

Enhancement-mode Si/SiGe electron quantum dots have been pursued extensively by many groups for \revEdit{their} potential in quantum computing. Most of the reported dot designs utilize multiple metal-gate layers and use Si/SiGe heterostructures with Ge concentration close to 30\%. Here we report the fabrication and low-temperature characterization...

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...

Albany is a multiphysics code constructed by assembling a set of reusable, general components. It is an implicit, unstructured grid finite element code that hosts a set of advanced features that are readily combined within a single analysis run. Albany uses template-based generic programming methods to provide extensibility and flexibility; it empl...

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 theory results [Salfi et al., Nat. Mater. 13, 605 (2014)]. Here, we show that multivalley effective mass theory, applied properly, does achieve close agreement with tight-binding results and...

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 quan...

For sixty years researchers have studied the electronic structure of donors
in silicon using the effective mass approximation. Despite a recent surge of
theoretical activity, inconsistent predictions and discrepancies with
experiment call into question the extent to which effective mass theory can
quantitatively describe donor physics. Earlier this...

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...

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...

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...

We report Pauli blockade in a multi electron silicon metal-oxide-semiconductor double quantum dot with an integrated charge sensor. Current is rectified up to a blockade energy of 0.18 ± 0.03 meV. The blockade energy is analogous to singlet-triplet splitting in a two electron double quantum dot. Built-in imbalances of tunnel rates in the MOS DQD ob...

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 Configura...

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 m...

The code development strategy, software design, and results from two application projects are presented for the Albany code: an implicit, unstructured grid, finite element code for the solution and analysis of partial differential equations. The driving strategy behind the development of Albany is the notion that it is increasingly possible, and ad...

Magnetic field inhomogeneity due to random polarization of quasi-static
local magnetic impurities is a major source of environmentally induced
error for singlet-triplet double quantum dot (DQD) spin qubits.
Moreover, for singlet-triplet qubits this error may depend on the
applied controls. This effect is significant when a static magnetic
field gra...

The combination of asymmetric tunnel rates and finite temperature can
shift the average charge occupation within a double quantum dot (DQD)
stability diagram. DQD charge sensing shows the transitions in electron
occupation dependence on gate bias. Applied source-drain bias further
introduces shifts in the charge transition lines including the forma...

We present the Quantum Computer Aided Design (QCAD) simulator that targets modeling quantum devices, particularly Si double quantum dots (DQDs) developed for quantum computing. The simulator core includes Poisson, Schrodinger, and Configuration Interaction solvers which can be run individually or combined self-consistently. The simulator is built u...

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...

We present results obtained using a newly developed semiclassical and
Poisson-Schrodinger simulation tool which is able to simultaneously
optimize many solution parameters. We discuss the benefit this
capability has on realistic device design, and report general trends
seen when targeting few-electron quantum dots in silicon and
silicon-germanium s...

Exchange interaction at the MOS interface has been proposed as a qubit
coupling approach for both MOS quantum dots and donor qubits. An
intrinsic source of disorder in the MOS system is the charge defects in
silicon dioxide, nanometers away from the interface and qubit electrons.
The presence of a charge defect so near the qubit can significantly
p...

We discuss trade-offs of different double quantum dot and charge sensor
lay-outs using computer assisted design (CAD). We use primarily a
semi-classical model, augmented with a self-consistent configuration
interaction method. Although CAD for quantum dots is difficult due to
uncontrolled factors (e.g., disorder), different ideal designs can still...

We report charge sensing measurements on a double quantum dot fabricated
in a silicon / silicon dioxide double top gated structure. Depletion
gates are used to laterally define a double quantum dot, and each dot
has an adjacent quantum point contact (QPC) electrometer for remote
detection of the dot occupation. For charge sensing, two techniques ha...

Quantum dots are artificial atoms used for a multitude of purposes. Charge
defects are commonly present and can significantly perturb the designed energy
spectrum and purpose of the dots. Voltage controlled exchange energy in silicon
double quantum dots (DQD) represents a system that is very sensitive to charge
position and is of interest for quant...

In this paper we present the impact of classical electronics constraints on a
solid-state quantum dot logical qubit architecture. Constraints due to routing
density, bandwidth allocation, signal timing, and thermally aware placement of
classical supporting electronics significantly affect the quantum error
correction circuit's error rate. We analyz...

We consider qubit coupling resulting from the capacitive coupling between two
double quantum dot (DQD) single-triplet qubits. Calculations of the coupling
when the two DQDs are detuned symmetrically or asymmetrically are performed
using a full configuration interaction (CI). The full CI reveals behavior that
is not observed by more commonly used ap...

Reducing the effects of electronics control error in double quantum dot (DQD) quantum bits (qubit) is a central challenge to the creation of a solid-state quantum computing architecture. We investigate a system of capacitively coupled DQDs which implement a variant of the controlled phase gate when using each DQD as a singlet-triplet qubit. We iden...

The singlet-triplet based silicon double quantum dot (DQD) is a promising system for implementing a long-lived and controllable quantum bit. The multiple valleys present in silicon, however, may complicate the operation of such a qubit if the valley splitting is small. The valley splitting is affected by a large number of factors including interfac...

We describe in detail a full configuration interaction (CI) method designed to analyze systems of quantum dots. This method is capable of exploring large regions of parameter space, like more approximate approaches such as Heitler London and Hund Mulliken, though it is not limited to weakly coupled dots. In particular, this method is well-suited to...

Minimizing the effects of noise is a central challenge to the creation of solid-state singlet-triplet double quantum dot (DQD) quantum bits (qubits). Charge noise, electronics error or inhomogeneous fields have all separately been addressed with different approaches. The demand for qubit operations robust to the combination of all noise sources pla...

Achieving low-error, exchange-interaction operations in quantum dots for
quantum computing imposes simultaneous requirements on the exchange energy's
dependence on applied voltages. A double quantum dot (DQD) qubit, approximated
with a quadratic potential, is solved using a full configuration interaction
method. This method is more accurate than He...