arXiv subjects

Kenneth R. Brown

Publications and source records attributed to Kenneth R. Brown.

At least 109 records · Page 6Linked to original sources

arXiv2018

Entangling an arbitrary pair of qubits in a long ion crystal

It is well established that the collective motion of ion crystals can be used as a quantum bus for multi-qubit entanglement. However, as the number of ions increases, it becomes difficult to directly entangle ions far apart and resolve all motional modes of the ion crystal. We introduce a scalable and flexible scheme for efficient entanglement between any pair of ions within a large ion chain, using an evenly distributed 50-ion crystal as an example. By performing amplitude and frequency modulation, we find high-fidelity pulse sequences that primarily drive a transverse motional mode with a wavelength of 4 ion spacings. We present two $500 μs$ pulses that can in theory suppress gate errors due to residual motion to below $10^{-4}$, and observe a trade-off between gate power and robustness against unwanted frequency offsets.

quant-ph↗

arXiv2018

Comparing Zeeman qubits to hyperfine qubits in the context of the surface code: $^{174}$Yb$^{+}$ and $^{171}$Yb$^{+}$

Many systems used for quantum computing possess additional states beyond those defining the qubit. Leakage out of the qubit subspace must be considered when designing quantum error correction codes. Here we consider trapped ion qubits manipulated by Raman transitions. Zeeman qubits do not suffer from leakage errors but are sensitive to magnetic fields to first-order. Hyperfine qubits can be encoded in clock states that are insensitive to magnetic fields to first-order, but spontaneous scattering during the Raman transition can lead to leakage. Here we compare a Zeeman qubit ($^{174}$Yb$^+$) to a hyperfine qubit ($^{171}$Yb$^+$) in the context of the surface code. We find that the number of physical qubits required to reach a specific logical qubit error can be reduced by using $^{174}$Yb$^+$ if the magnetic field can be stabilized with fluctuations smaller than $10$ $μ$G.

quant-ph↗

arXiv2018

Direct measurement of Bacon-Shor code stabilizers

A Bacon-Shor code is a subsystem quantum error-correcting code on an $L \times L$ lattice where the $2(L-1)$ weight-$2L$ stabilizers are usually inferred from the measurements of $(L-1)^2$ weight-2 gauge operators. Here we show that the stabilizers can be measured directly and fault tolerantly with bare ancillary qubits by constructing circuits that follow the pattern of gauge operators. We then examine the implications of this method for small quantum error-correcting codes by comparing distance 3 versions of the rotated surface code and the Bacon-Shor code with the standard depolarizing model and in the context of a trapped ion quantum computer. We find that for a simple circuit of prepare, error correct and measure the Bacon-Shor code outperforms the surface code by requiring fewer qubits, taking less time, and having a lower error rate.

quant-ph↗

arXiv2017

Robust two-qubit gates in a linear ion crystal using a frequency-modulated driving force

In an ion trap quantum computer, collective motional modes are used to entangle two or more qubits in order to execute multi-qubit logical gates. Any residual entanglement between the internal and motional states of the ions results in loss of fidelity, especially when there are many spectator ions in the crystal. We propose using a frequency-modulated (FM) driving force to minimize such errors. In simulation, we obtained an optimized FM two-qubit gate that can suppress errors to less than 0.01\% and is robust against frequency drifts over $\pm$1 kHz. Experimentally, we have obtained a two-qubit gate fidelity of $98.3(4)\%$, a state-of-the-art result for two-qubit gates with 5 ions.

physics.atom-ph↗

arXiv2017

Fault Tolerance with Bare Ancillae for a [[7,1,3]] Code

We present a [[7, 1, 3]] quantum error-correcting code that is able to achieve fault-tolerant syndrome measurement using one ancillary qubit per stabilizer for an error model of independent single-qubit Pauli errors. All single-qubit Pauli errors on the ancillary qubits propagate to form exclusively correctable errors on the data qubits. The situation changes for error models with two-qubit Pauli errors. We compare the level-1 logical error rates under two noise models: the standard Pauli symmetric depolarizing error model and an anisotropic error model. The anisotropic model is motivated by control errors on two-qubit gates commonly applied to trapped ion qubits. We find that one ancillary qubit per syndrome measurement is sufficient for fault-tolerance for the anisotropic error, but is not sufficient for the standard depolarizing errors. We then show how to achieve fault tolerance for the standard depolarizing errors by adding flag qubits to check for errors on select ancilary qubits. Our results on this [[7, 1, 3]] code demonstrates how physically motivated noise models may simplify fault-tolerent protocols.

quant-ph↗

arXiv2017

Optimized Surface Code Communication in Superconducting Quantum Computers

Quantum computing (QC) is at the cusp of a revolution. Machines with 100 quantum bits (qubits) are anticipated to be operational by 2020 [googlemachine,gambetta2015building], and several-hundred-qubit machines are around the corner. Machines of this scale have the capacity to demonstrate quantum supremacy, the tipping point where QC is faster than the fastest classical alternative for a particular problem. Because error correction techniques will be central to QC and will be the most expensive component of quantum computation, choosing the lowest-overhead error correction scheme is critical to overall QC success. This paper evaluates two established quantum error correction codes---planar and double-defect surface codes---using a set of compilation, scheduling and network simulation tools. In considering scalable methods for optimizing both codes, we do so in the context of a full microarchitectural and compiler analysis. Contrary to previous predictions, we find that the simpler planar codes are sometimes more favorable for implementation on superconducting quantum computers, especially under conditions of high communication congestion.

quant-ph↗

arXiv2017

Reassigning the CaH$^+$ 1$^{1}Σ\rightarrow$ 2$^{1}Σ$ vibronic transition with CaD$^+$

We observe vibronic transitions in CaD$^+$ between the 1$^{1}Σ$ and 2$^{1}Σ$ electronic states by resonance enhanced multiphoton photodissociation spectroscopy in a Coulomb crystal. The vibronic transitions are compared with previous measurements on CaH$^+$. The result is a revised assignment of the CaH$^+$ vibronic levels and a disagreement with CASPT2 theoretical calculations by approximately 700 cm$^{-1}$.

physics.atom-ph↗

arXiv2017

Analytical Error Analysis of Clifford Gates by the Fault-Path Tracer Method

We estimate the success probability of quantum protocols composed of Clifford operations in the presence of Pauli errors. Our method is derived from the fault-point formalism previously used to determine the success rate of low-distance error correction codes. Here we apply it to a wider range of quantum protocols and identify circuit structures that allow for efficient calculation of the exact success probability and even the final distribution of output states. As examples, we apply our method to the Bernstein-Vazirani algorithm and the Steane [[7,1,3]] quantum error correction code and compare the results to Monte Carlo simulations.

quant-ph↗

arXiv2016

Trapping and Sympathetic Cooling of Boron Ions

We demonstrate the trapping and sympathetic cooling of B$^{+}$ ions in a Coulomb crystal of laser-cooled Ca$^{+}$, We non-destructively confirm the presence of the both B$^+$ isotopes by resonant excitation of the secular motion. The B$^{+}$ ions are loaded by ablation of boron and the secular excitation spectrum also reveals features consistent with ions of the form B$_{n}^{+}$.

physics.atom-ph↗

arXiv2016

Vibronic spectroscopy of sympathetically cooled CaH$^+$

We report the measurement of the 1$^{1}Σ\longrightarrow$ 2$^{1}Σ$ transition of CaH$^+$ by resonance-enhanced photodissociation of CaH$^+$ that is co-trapped with laser-cooled Ca$^+$ . We observe four resonances that we assign to transitions from the vibrational $v$=0 ground state to the $v'$=1-4 excited states based on theoretical predictions. A simple theoretical model that assumes instantaneous dissociation after resonant excitation yield results in good agreement with the observed spectral features except for the unobserved $v'$=0 peak. The resolution of our experiment is limited by the mode-locked excitation laser, but this survey spectroscopy enables future rotationally resolved studies with applications in astrochemistry and precision measurement.

physics.atom-ph↗

arXiv2016

Errors and pseudo-thresholds for incoherent and coherent noise

We compare the effect of single qubit incoherent and coherent errors on the logical error rate of the Steane [[7,1,3]] quantum error correction code by performing an exact full-density-matrix simulation of an error correction step. We find that the effective 1-qubit process matrix at the logical level reveals the key differences between the error models and provides insight into why the Pauli twirling approximation is a good approximation for incoherent errors and a poor approximation for coherent ones. Approximate channels composed of Clifford operations and Pauli measurement operators that are pessimistic at the physical level result in pessimistic error rates at the logical level. In addition, we observe that the pseudo-threshold can differ by a factor of five depending on whether the error is calculated using the fidelity or the distance.

quant-ph↗

arXiv2015

Modulating carrier and sideband coupling strengths in a standing wave gate beam

We control the relative coupling strength of carrier and first order motional sideband interactions of a trapped ion by placing it in a resonant optical standing wave. Our configuration uses the surface of a microfabricated chip trap as a mirror, avoiding technical challenges of in-vacuum optical cavities. Displacing the ion along the standing wave, we show a periodic suppression of the carrier and sideband transitions with the cycles for the two cases $180^\circ$ out of phase with each other. This technique allows for suppression of off-resonant carrier excitations when addressing the motional sidebands, with applications in quantum simulation and quantum control. Using the standing wave fringes, we measure the relative ion height as a function of applied electric field, allowing for a precise measurement of ion displacement and, combined with measured micromotion amplitudes, a validation of trap numerical models.

quant-ph↗

arXiv2015

Observation of vibrational overtones by single molecule resonant photodissociation

Molecular ions can be held in a chain of laser-cooled atomic ions by sympathetic cooling. This system is ideal for performing high-precision molecular spectroscopy with applications in astrochemistry and fundamental physics. Here we show that this same system can be coupled with a broadband laser to discover new molecular transitions. We use three-ion chains of Ca$^{+}$ and CaH$^{+}$ to observe vibrational transitions via resonance enhanced multiphoton dissociation detected by Ca$^{+}$ fluorescence. Based on theoretical calculations, we assign the observed peaks to the transition from the ground vibrational state, $ν=0$, to $ν=9$ and $ν=10$. Our method allows us to track single molecular events, and it can be extended to work with any molecule by using normal mode frequency shifts to detect the dissociation. This survey spectroscopy serves as a bridge to the precision spectroscopy required for molecular ion control.

physics.atom-ph↗

arXiv2015

Error Compensation of Single-Qubit Gates in a Surface Electrode Ion Trap Using Composite Pulses

The fidelity of laser-driven quantum logic operations on trapped ion qubits tend to be lower than microwave-driven logic operations due to the difficulty of stabilizing the driving fields at the ion location. Through stabilization of the driving optical fields and use of composite pulse sequences, we demonstrate high fidelity single-qubit gates for the hyperfine qubit of a $^{171}\text{Yb}^+$ ion trapped in a microfabricated surface electrode ion trap. Gate error is characterized using a randomized benchmarking protocol, and an average error per randomized Clifford group gate of $3.6(3)\times10^{-4}$ is measured. We also report experimental realization of palindromic pulse sequences that scale efficiently in sequence length.

quant-ph↗

arXiv2015

Magic State Distillation and Gate Compilation in Quantum Algorithms for Quantum Chemistry

Quantum algorithms for quantum chemistry map the dynamics of electrons in a molecule to the dynamics of a coupled spin system. To reach chemical accuracy for interesting molecules, a large number of quantum gates must be applied which implies the need for quantum error correction and fault-tolerant quantum computation. Arbitrary fault-tolerant operations can be constructed from a small, universal set of fault-tolerant operations by gate compilation. Quantum chemistry algorithms are compiled by decomposing the dynamics of the coupled spin-system using a Trotter formula, synthesizing the decomposed dynamics using Clifford operations and single-qubit rotations, and finally approximating the single-qubit rotations by a sequence of fault-tolerant single-qubit gates. Certain fault-tolerant gates rely on the preparation of specific single-qubit states referred to as magic states. As a result, gate compilation and magic state distillation are critical for solving quantum chemistry problems on a quantum computer. We review recent progress that has improved the efficiency of gate compilation and magic state distillation by orders of magnitude.

quant-ph↗

arXiv2015

Comparison of a quantum error correction threshold for exact and approximate errors

Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code. Physical noise sources are efficiently approximated by random insertions of Pauli operators. For a single qubit, more accurate approximations that still allow for efficient simulation can be obtained by including Clifford operators and Pauli operators conditional on measurement in the noise model. We examine the feasibility of employing these expanded error approximations to obtain better threshold estimates. We calculate the level-1 pseudothreshold for the Steane [[7,1,3]] code for amplitude damping and dephasing along a non-Clifford axis. The expanded channels estimate the actual channel action more accurately than the Pauli channels before error correction. However, after error correction, the Pauli twirling approximation yields very accurate estimates of the performance of quantum error-correcting protocols in the presence of the actual noise channel.

quant-ph↗

arXiv2014

Sympathetic cooling of molecular ion motion to the ground state

We demonstrate sympathetic sideband cooling of a $^{40}$CaH$^{+}$ molecular ion co-trapped with a $^{40}$Ca$^{+}$ atomic ion in a linear Paul trap. Both axial modes of the two-ion chain are simultaneously cooled to near the ground state of motion. The center of mass mode is cooled to an average quanta of harmonic motion $\overline{n}_{\mathrm{COM}} = 0.13 \pm 0.03$, corresponding to a temperature of $12.47 \pm 0.03 ~μ$K. The breathing mode is cooled to $\overline{n}_{\mathrm{BM}} = 0.05 \pm 0.02$, corresponding to a temperature of $15.36 \pm 0.01~μ$K.

physics.atom-ph↗

arXiv2014

Making Classical Ground State Spin Computing Fault-Tolerant

We examine a model of classical deterministic computing in which the ground state of the classical system is a spatial history of the computation. This model is relevant to quantum dot cellular automata as well as to recent universal adiabatic quantum computing constructions. In its most primitive form, systems constructed in this model cannot compute in an error free manner when working at non-zero temperature. However, by exploiting a mapping between the partition function for this model and probabilistic classical circuits we are able to show that it is possible to make this model effectively error free. We achieve this by using techniques in fault-tolerant classical computing and the result is that the system can compute effectively error free if the temperature is below a critical temperature. We further link this model to computational complexity and show that a certain problem concerning finite temperature classical spin systems is complete for the complexity class Merlin-Arthur. This provides an interesting connection between the physical behavior of certain many-body spin systems and computational complexity.

cond-mat.stat-mech↗