arXiv subjects

Kenneth R. Brown

Publications and source records attributed to Kenneth R. Brown.

At least 55 records · Page 3Linked to original sources

arXiv2024

Few-Shot, Robust Calibration of Single Qubit Gates Using Bayesian Robust Phase Estimation

Accurate calibration of control parameters in quantum gates is crucial for high-fidelity operations, yet it represents a significant time and resource challenge, necessitating periods of downtime for quantum computers. Robust Phase Estimation (RPE) has emerged as a practical and effective calibration technique aimed at tackling this challenge. It combines a provably efficient number of control pulses with a classical post-processing algorithm to estimate the phase accumulated by a quantum gate. We introduce Bayesian Robust Phase Estimation (BRPE), an innovative approach that integrates Bayesian parameter estimation into the classical post-processing phase to reduce the sampling overhead. Our numerical analysis shows that BRPE markedly reduces phase estimation errors, requiring approximately $50\%$ fewer samples than standard RPE. Specifically, in an ideal, noise-free setting, it achieves up to a $96\%$ reduction in average absolute estimation error for a fixed sample cost of $88$ shots when compared to RPE. Under a depolarizing noise model, it attains up to a $47\%$ reduction for a fixed cost of $176$ shots. Additionally, we adapt BRPE for Ramsey spectroscopy applications and successfully implement it experimentally in a trapped ion system.

quant-ph↗

arXiv2024

Design and characterization of individual addressing optics based on multi-channel acousto-optic modulator for $^{171}$Yb$^+$ qubits

We present the design and characterization of individual addressing optics based on a multi-channel acousto-optic modulator (AOM) for trapped ytterbium-171 ions. The design parameters of the individual addressing system were determined based on the tradeoff between the expected crosstalk and the required numerical aperture of the projection objective lens. The target beam diameter and separation were 1.90 $μ$m and 4.28 $μ$m, respectively. The individual beams shaped by the projection optics were characterized by an imaging sensor and a field probe ion. The resulting effective beam diameters and separations were approximately 2.34--2.36 $μ$m and 4.31 $μ$m, respectively, owing to residual aberration.

quant-ph↗

arXiv2024

Optimization tools for distance-preserving flag fault-tolerant error correction

Lookup table decoding is fast and distance-preserving, making it attractive for near-term quantum computer architectures with small-distance quantum error-correcting codes. In this work, we develop several optimization tools that can potentially reduce the space and time overhead required for flag fault-tolerant quantum error correction (FTQEC) with lookup table decoding on Calderbank-Shor-Steane (CSS) codes. Our techniques include the compact lookup table construction, the Meet-in-the-Middle technique, the adaptive time decoding for flag FTQEC, the classical processing technique for flag information, and the separated $X$ and $Z$ counting technique. We evaluate the performance of our tools using numerical simulation of hexagonal color codes of distances 3, 5, 7, and 9 under circuit-level noise. Combining all tools can result in more than an order of magnitude increase in pseudothreshold for the hexagonal color code of distance 9, from $(1.34 \pm 0.01) \times 10^{-4}$ to $(1.42 \pm 0.12) \times 10^{-3}$.

quant-ph↗

arXiv2024

A comparison of continuous and pulsed sideband cooling on an electric quadrupole transition

Sideband cooling enables preparation of trapped ion motion near the ground state and is essential for many scientific and technological applications of trapped ion devices. Here, we study the efficiency of continuous and pulsed sideband cooling using both first- and second-order sidebands applied to an ion where the motion starts outside the Lamb-Dicke regime. We find that after optimizing these distinct cooling methods, pulsed and continuous cooling achieve similar results based on simulations and experiments with a $^{40}$Ca$^+$ ion. We consider optimization of both average phonon number $\overline{n}$ and population in the ground state. We also demonstrate the disparity between $\overline{n}$ as measured by the sideband ratio method of trapped ion thermometry and the $\overline{n}$ found by averaging over the ion's motional state distribution.

physics.atom-ph↗

arXiv2023

Comparing Shor and Steane Error Correction Using the Bacon-Shor Code

Quantum states can quickly decohere through interaction with the environment. Quantum error correction is a method for preserving coherence through active feedback. Quantum error correction encodes the quantum information into a logical state with a high-degree of symmetry. Perturbations are first detected by measuring the symmetries of the quantum state and then corrected by applying a set of gates based on the measurements. In order to measure the symmetries without perturbing the data, ancillary quantum states are required. Shor error correction uses a separate quantum state for the measurement of each symmetry. Steane error correction maps the perturbations onto a logical ancilla qubit, which is then measured to check several symmetries simultaneously. Here we experimentally compare Shor and Steane correction of bit flip errors using the Bacon-Shor code implemented in a chain of 23 trapped atomic ions. We find that the Steane error correction provides better logical error rates after a single-round of error correction and less disturbance to the data qubits without error correction.

quant-ph↗

arXiv2023

Robust Syndrome Extraction via BCH Encoding

Quantum data-syndrome (QDS) codes are a class of quantum error-correcting codes that protect against errors both on the data qubits and on the syndrome itself via redundant measurement of stabilizer group elements. One way to define a QDS code is to choose a syndrome measurement code, a classical block code that encodes the syndrome of the underlying quantum code by defining additional stabilizer measurements. We propose the use of primitive narrow-sense BCH codes as syndrome measurement codes. We show that these codes asymptotically require $O(t\log\ell)$ extra measurements, where $\ell$ is the number of stabilizer generators of the quantum code and $t$ is the number of errors corrected by the BCH code. Previously, the best known general method of constructing QDS codes out of quantum codes requires $O(t^3\log\ell)$ extra measurements. As the number of additional syndrome measurements is a reasonable metric for the amount of additional time a general QDS code requires, we conclude that our construction protects against the same number of syndrome errors with significantly less time overhead.

quant-ph↗

arXiv2023

Single-shot error correction on toric codes with high-weight stabilizers

For quantum error correction codes the required number of measurement rounds typically increases with the code distance when measurements are faulty. Single-shot error correction allows for an error threshold with only one round of noisy syndrome measurements regardless of the code size. Here we implement single-shot check operators for toric codes. The single-shot checks are constructed by Gaussian elimination following Campbell [Campbell, 2019]. The single-shot check operators result in a sustainable threshold at 5.62% for an error model with noisy measurements, outperforming the conventional toric code check operators with multiple rounds of noisy measurement. The cost of the transformation is non-local high-weight stabilizer generators. We then consider a gate-based error model that leads to increased measurement error with stabilizer weight. Here we find no single-shot threshold behavior and instead find the code family will have an optimal code size for a fixed error rate. For this error model, the conventional check operators with multiple measurements yields a lower logical error rate.

quant-ph↗

arXiv2023

CAFQA: A classical simulation bootstrap for variational quantum algorithms

This work tackles the problem of finding a good ansatz initialization for Variational Quantum Algorithms (VQAs), by proposing CAFQA, a Clifford Ansatz For Quantum Accuracy. The CAFQA ansatz is a hardware-efficient circuit built with only Clifford gates. In this ansatz, the parameters for the tunable gates are chosen by searching efficiently through the Clifford parameter space via classical simulation. The resulting initial states always equal or outperform traditional classical initialization (e.g., Hartree-Fock), and enable high-accuracy VQA estimations. CAFQA is well-suited to classical computation because: a) Clifford-only quantum circuits can be exactly simulated classically in polynomial time, and b) the discrete Clifford space is searched efficiently via Bayesian Optimization. For the Variational Quantum Eigensolver (VQE) task of molecular ground state energy estimation (up to 18 qubits), CAFQA's Clifford Ansatz achieves a mean accuracy of nearly 99% and recovers as much as 99.99% of the molecular correlation energy that is lost in Hartree-Fock initialization. CAFQA achieves mean accuracy improvements of 6.4x and 56.8x, over the state-of-the-art, on different metrics. The scalability of the approach allows for preliminary ground state energy estimation of the challenging chromium dimer (Cr$_2$) molecule. With CAFQA's high-accuracy initialization, the convergence of VQAs is shown to accelerate by 2.5x, even for small molecules. Furthermore, preliminary exploration of allowing a limited number of non-Clifford (T) gates in the CAFQA framework, shows that as much as 99.9% of the correlation energy can be recovered at bond lengths for which Clifford-only CAFQA accuracy is relatively limited, while remaining classically simulable.

quant-ph↗

arXiv2023

Adaptive syndrome measurements for Shor-style error correction

The Shor fault-tolerant error correction (FTEC) scheme uses transversal gates and ancilla qubits prepared in the cat state in syndrome extraction circuits to prevent propagation of errors caused by gate faults. For a stabilizer code of distance $d$ that can correct up to $t=\lfloor(d-1)/2\rfloor$ errors, the traditional Shor scheme handles ancilla preparation and measurement faults by performing syndrome measurements until the syndromes are repeated $t+1$ times in a row; in the worst-case scenario, $(t+1)^2$ rounds of measurements are required. In this work, we improve the Shor FTEC scheme using an adaptive syndrome measurement technique. The syndrome for error correction is determined based on information from the differences of syndromes obtained from consecutive rounds. Our protocols that satisfy the strong and the weak FTEC conditions require no more than $(t+3)^2/4-1$ rounds and $(t+3)^2/4-2$ rounds, respectively, and are applicable to any stabilizer code. Our simulations of FTEC protocols with the adaptive schemes on hexagonal color codes of small distances verify that our protocols preserve the code distance, can increase the pseudothreshold, and can decrease the average number of rounds compared to the traditional Shor scheme. We also find that for the code of distance $d$, our FTEC protocols with the adaptive schemes require no more than $d$ rounds on average.

quant-ph↗

arXiv2023

Quantum Error Correction with Metastable States of Trapped Ions Using Erasure Conversion

Erasures, or errors with known locations, are a more favorable type of error for quantum error-correcting codes than Pauli errors. Converting physical noise into erasures can significantly improve the performance of quantum error correction. Here we apply the idea of performing erasure conversion by encoding qubits into metastable atomic states, proposed by Wu, Kolkowitz, Puri, and Thompson [Nat. Comm. 13, 4657 (2022)], to trapped ions. We suggest an erasure-conversion scheme for metastable trapped-ion qubits and develop a detailed model of various types of errors. We then compare the logical performance of ground and metastable qubits on the surface code under various physical constraints, and conclude that metastable qubits may outperform ground qubits when the achievable laser power is higher for metastable qubits.

quant-ph↗

arXiv2023

Quantum Simulation of Polarized Light-induced Electron Transfer with A Trapped-ion Qutrit System

Electron transfer within and between molecules is crucial in chemistry, biochemistry, and energy science. This study describes a quantum simulation method that explores the influence of light polarization on the electron transfer between two molecules. By implementing precise and coherent control among the quantum states of trapped atomic ions, we can induce quantum dynamics that mimic the electron transfer dynamics in molecules. We use $3$-level systems (qutrits), rather than traditional two-level systems (qubits) to enhance the simulation efficiency and realize high-fidelity simulations of electron transfer dynamics. We treat the quantum interference between the electron coupling pathways from a donor with two degenerate excited states to an acceptor and analyze the transfer efficiency. We also examine the potential error sources that enter the quantum simulations. The trapped ion systems have favorable scalings with system size compared to those of classical computers, promising access to electron-transfer simulations of increasing richness.

quant-ph↗

arXiv2023

Simulating conical intersections with trapped ions

Conical intersections are common in molecular physics and photochemistry, and are often invoked to explain observed reaction products. A conical intersection can occur when an excited electronic potential energy surface intersects with the ground electronic potential energy surface in the coordinate space of the nuclear positions. Theory predicts that the conical intersection will result in a geometric phase for a wavepacket on the ground potential energy surface. Although conical intersections have been observed experimentally, the geometric phase has not been observed in a molecular system. Here we use a trapped atomic ion system to perform a quantum simulation of a conical intersection. The internal state of a trapped atomic ion serves as the electronic state and the motion of the atomic nuclei are encoded into the normal modes of motion of the ions. The simulated electronic potential is constructed by applying state-dependent forces to the ion with a near-resonant laser. We experimentally observe the geometric phase on the ground-state surface using adiabatic state preparation followed by motional state measurement. Our experiment shows the advantage of combining spin and motion degrees of freedom in a quantum simulator.

quant-ph↗

arXiv2023

Designing Filter Functions of Frequency-Modulated Pulses for High-Fidelity Two-Qubit Gates in Ion Chains

High-fidelity two-qubit gates in quantum computers are often hampered by fluctuating experimental parameters. The effects of time-varying parameter fluctuations lead to coherent noise on the qubits, which can be suppressed by designing control signals with appropriate filter functions. Here, we develop filter functions for Mølmer-Sørensen gates of trapped-ion quantum computers that accurately predict the change in gate error due to small parameter fluctuations at any frequency. We then design the filter functions of frequency-modulated laser pulses, and compare this method with pulses that are robust to static offsets of the motional-mode frequencies. Experimentally, we measure the noise spectrum of the motional modes and use it for designing the filter functions, which improves the gate fidelity from 99.23(7)% to 99.55(7)% in a five-ion chain.

quant-ph↗

arXiv2022

Adiabatically controlled motional states of a ground-state cooled CaO$^{+}$ and Ca$^{+}$ trapped ion chain

Control of the external degree of freedom of trapped molecular ions is a prerequisite for their promising applications to spectroscopy, precision measurements of fundamental constants, and quantum information technology. Here, we demonstrate near ground-state cooling of the axial motional modes of a calcium mono-oxide ion via sympathetic sideband cooling with a co-trapped calcium ion. We also show that the phonon state of the axial out-of-phase mode of the ion chain is maintained while the mode frequency is adiabatically ramped up and down. The adiabatic ramping of the motional mode frequency is a prerequisite for searching for the proposed molecular dipole-phonon interaction.

physics.atom-ph↗

arXiv2022

Functional Simulation of Real-Time Quantum Control Software

Modern quantum computers rely heavily on real-time control systems for operation. Software for these systems is becoming increasingly more complex due to the demand for more features and more real-time devices to control. Unfortunately, testing real-time control software is often a complex process, and existing simulation software is not usable or practical for software testing. For this purpose, we implemented an interactive simulator that simulates signals at the application programming interface level. We show that our simulation infrastructure simulates kernels 6.9 times faster on average compared to execution on hardware, while the position of the timeline cursor is simulated with an average accuracy of 97.9% when choosing the appropriate configuration.

quant-ph↗

arXiv2022

Modular Software for Real-Time Quantum Control Systems

Real-time control software and hardware is essential for operating quantum computers. In particular, the software plays a crucial role in bridging the gap between quantum programs and the quantum system. Unfortunately, current control software is often optimized for a specific system at the cost of flexibility and portability. We propose a systematic design strategy for modular real-time quantum control software and demonstrate that modular control software can reduce the execution time overhead of kernels by 63.3% on average while not increasing the binary size. Our analysis shows that modular control software for two distinctly different systems can share between 49.8% and 91.0% of covered code statements. To demonstrate the modularity and portability of our software architecture, we run a portable randomized benchmarking experiment on two different ion-trap quantum systems.

quant-ph↗

arXiv2022

Angle-robust Two-Qubit Gates in a Linear Ion Crystal

In trapped-ion quantum computers, two-qubit entangling gates are generated by applying spin-dependent force which uses phonons to mediate interaction between the internal states of the ions. To maintain high-fidelity two-qubit gates under fluctuating experimental parameters, robust pulse-design methods are applied to remove the residual spin-motion entanglement in the presence of motional mode frequency drifts. Here we propose an improved pulse-design method that also guarantees the robustness of the two-qubit rotation angle against uniform mode frequency drifts by combining pulses with opposite sensitivity of the angle to mode frequency drifts. We experimentally measure the performance of the designed gates and see an improvement on both gate fidelity and gate performance under uniform mode frequency offsets.

quant-ph↗

arXiv2022

Mesh-Free Interpolant Observables for Continuous Data Assimilation

This paper considers a nudging-based scheme for data assimilation for the two-dimensional (2D) Navier-Stokes equations (NSE) with periodic boundary conditions and studies the synchronization of the signal produced by this algorithm with the true signal, to which the observations correspond, in all higher-order Sobolev topologies. This work complements previous results in the literature where conditions were identified under which synchronization is guaranteed either with respect to only the $H^1$--topology, in the case of general observables, or to the analytic Gevrey topology, in the case of spectral observables. To accommodate the property of synchronization in the stronger topologies, the framework of general interpolant observable operators, originally introduced by Azouani, Olson, and Titi, is expanded to a far richer class of operators. A significant effort is dedicated to the development of this more expanded framework, specifically, their basic approximation properties, the identification of subclasses of such operators relevant to obtaining synchronization, as well as the detailed relation between the structure of these operators and the system regarding the syncrhonization property. One of the main features of this framework is its "mesh-free" aspect, which allows the observational data itself to dictate the subdivision of the domain. Lastly, estimates for the radius of the absorbing ball of the 2D NSE in all higher-order Sobolev norms are obtained, thus properly generalizing previously known bounds; such estimates are required for establishing the synchronization property of the algorithm in the higher-order topologies.

math.AP↗