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Andrew J. Landahl

Publications and source records attributed to Andrew J. Landahl.

At least 19 recordsLinked to original sources
arXiv2026

Solovay Kitaev Algorithm and Randomized Compilation

We analyze the use of the Solovay Kitaev (SK) algorithm to generate an ensemble of one qubit rotations over which to perform randomized compilation. We perform simulations to compare the trace distance between the quantum state resulting from an ideal one qubit $R_{Z}$ rotation and discrete SK decompositions. We find that this simple randomized gate synthesis algorithm can reduce the approximation error of these rotations in the absence of gate errors in simulation by at least a factor of two compared to a naive gate synthesis algorithm. We test the technique under the effects of a simple coherent noise model and find that it can mitigate coherent noise. We also run our algorithm on Sandia National Laboratories' QSCOUT trapped-ion device and find that randomization is able to help in the presence of realistic noise sources.

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arXiv2025

A small and interesting architecture for early fault-tolerant quantum computers

We present an architecture for early fault-tolerant quantum computers based on the smallest interesting colour code (Earl Campbell, 2016). It realizes a universal logical gate set consisting of single-qubit measurements and preparations in the X and Z bases, single-qubit Hadamard (H) gates, and three-qubit controlled-controlled-Z (CCZ) gates. State teleportations between [[4, 2, 2]] (2D) and [[8, 3, 2]] (3D) error-detecting color codes allow one to make use of the respective transversal H and CCZ gates that these codes possess. As such, minimizing the number of logical quantum teleportation operations, not the number of logical quantum non-Clifford gates, is the relevant optimization goal. To help hardware developers characterize this architecture, we also provide an experimental protocol tailored to testing logical quantum circuits expressed in it.

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arXiv2024

Error mitigation, optimization, and extrapolation on a trapped ion testbed

Current noisy intermediate-scale quantum (NISQ) trapped-ion devices are subject to errors which can significantly impact the accuracy of calculations if left unchecked. A form of error mitigation called zero noise extrapolation (ZNE) can decrease an algorithm's sensitivity to these errors without increasing the number of required qubits. Here, we explore different methods for integrating this error mitigation technique into the Variational Quantum Eigensolver (VQE) algorithm for calculating the ground state of the HeH+ molecule at 0.8 Angstrom in the presence of realistic noise. Using the Quantum Scientific Computing Open User Testbed (QSCOUT) trapped-ion device, we test three methods of scaling noise for extrapolation: time-stretching the two-qubit gates, scaling the sideband amplitude parameter, and inserting two-qubit gate identity operations into the ansatz circuit. We find time-stretching and sideband amplitude scaling fail to scale the noise on our particular hardware in a way that can be directly extrapolated to zero noise. Scaling our noise with global gate identity insertions and extrapolating after variational optimization, we achieve an estimate of the ground state energy within -0.004 +- 0.04 Hartree; outside chemical accuracy, but greatly improved over our non-error-mitigated estimate with error 0.127 +- 0.008 Hartree. Our results show that the efficacy of this error mitigation technique depends on choosing the correct implementation for a given device architecture.

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arXiv2024

Requirements for building effective Hamiltonians using quantum-enhanced density matrix downfolding

Density matrix downfolding (DMD) is a technique for regressing low-energy effective Hamiltonians from quantum many-body Hamiltonians. One limiting factor in the accuracy of classical implementations of DMD is the presence of difficult-to-quantify systematic errors attendant to sampling the observables of quantum many-body systems on an approximate low-energy subspace. We propose a hybrid quantum-classical protocol for circumventing this limitation, relying on the prospective ability of quantum computers to efficiently prepare and sample from states in well-defined low-energy subspaces with systematically improvable accuracy. We introduce three requirements for when this is possible, including a notion of compressibility that quantifies features of Hamiltonians and low-energy subspaces thereof for which quantum DMD might be efficient. Assuming that these requirements are met, we analyze design choices for our protocol and provide resource estimates for implementing quantum-enhanced DMD on both the doped 2-D Fermi-Hubbard model and an ab initio model of a cuprate superconductor.

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arXiv2023

Logical fermions for fault-tolerant quantum simulation

We show how to absorb fermionic quantum simulation's expensive fermion-to-qubit mapping overhead into the overhead already incurred by surface-code-based fault-tolerant quantum computing. The key idea is to process information in surface-code twist defects, which behave like logical Majorana fermions. Our approach encodes Dirac fermions, a key data type for simulation applications, directly into logical Majorana fermions rather than atop a logical qubit layer in the architecture. Using quantum simulation of the $N$-fermion 2D Fermi-Hubbard model as an exemplar, we demonstrate two immediate algorithmic improvements. First, by preserving the model's locality at the logical level, we reduce the asymptotic Trotter-Suzuki quantum circuit depth from $\mathcal{O}(\sqrt{N})$ in a typical Jordan-Wigner encoding to $\mathcal{O}(1)$ in our encoding. Second, by exploiting optimizations manifest for logical fermions but less obvious for logical qubits, we reduce the $T$-count of the block-encoding \textsc{select} oracle by 20\% over standard implementations, even when realized by logical qubits and not logical fermions.

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arXiv2023

JaqalPaw: A Guide to Defining Pulses and Waveforms for Jaqal

One of the many challenges of developing an open user testbed such as QSCOUT is providing an interface that maintains simplicity without compromising expressibility or control. This interface comprises two distinct elements: a quantum assembly language designed for specifying quantum circuits at the gate level, and a low-level counterpart used for describing gates in terms of waveforms that realize specific quantum operations. Jaqal, or "Just another quantum assembly language," is the language used in QSCOUT for gate-level descriptions of quantum circuits. JaqalPaw, or "Jaqal pulses and waveforms," is its pulse-level counterpart. This document concerns the latter, and presents a description of the tools needed for precisely defining the underlying waveforms associated with a gate primitive.

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arXiv2020

Just another quantum assembly language (Jaqal)

The Quantum Scientific Computing Open User Testbed (QSCOUT) is a trapped-ion quantum computer testbed realized at Sandia National Laboratories on behalf of the Department of Energy's Office of Science and its Advanced Scientific Computing (ASCR) program. Here we describe Jaqal, for Just another quantum assembly language, the programming language we invented to specify programs executed on QSCOUT. Jaqal is useful beyond QSCOUT---it can support mutliple hardware targets because it offloads gate names and their pulse-sequence definitions to external files. We describe the capabilities of the Jaqal language, our approach in designing it, and the reasons for its creation. To learn more about QSCOUT, Jaqal, or JaqalPaq, the metaprogramming Python package we developed for Jaqal, please visit https://qscout.sandia.gov, https://gitlab.com/jaqal, or send an e-mail to qscout@sandia.gov.

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arXiv2020

Jaqal, the Quantum Assembly Language for QSCOUT

QSCOUT is the Quantum Scientific Computing Open User Testbed, a trapped-ion quantum computer testbed realized at Sandia National Laboratories on behalf of the Department of Energy's Office of Science and its Advanced Scientific Computing (ASCR) program. Jaqal, for Just Another Quantum Assembly Language, is the programming language used to specify programs executed on QSCOUT. This document contains a specification of Jaqal along with a summary of QSCOUT 1.0 capabilities, example Jaqal programs, and plans for possible future extensions. To learn more about QSCOUT and the Jaqal language developed for it, please visit qscout.sandia.gov or send an e-mail to qscout@sandia.gov.

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arXiv2014

Quantum computing by color-code lattice surgery

We demonstrate how to use lattice surgery to enact a universal set of fault-tolerant quantum operations with color codes. Along the way, we also improve existing surface-code lattice-surgery methods. Lattice-surgery methods use fewer qubits and the same time or less than associated defect-braiding methods. Furthermore, per code distance, color-code lattice surgery uses approximately half the qubits and the same time or less than surface-code lattice surgery. Color-code lattice surgery can also implement the Hadamard and phase gates in a single transversal step---much faster than surface-code lattice surgery can. Against uncorrelated circuit-level depolarizing noise, color-code lattice surgery uses fewer qubits to achieve the same degree of fault-tolerant error suppression as surface-code lattice surgery when the noise rate is low enough and the error suppression demand is high enough.

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arXiv2014

Adiabatic topological quantum computing

Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic excitations will be created that will disorder the encoded quantum information. Here we explore this question in detail by studying adiabatic code deformations on Hamiltonians based on topological codes, notably Kitaev's surface codes and the more recently discovered color codes. We develop protocols that enable universal quantum computing by adiabatic evolution in a way that keeps the energy gap of the system constant with respect to the computation size and introduces only simple local Hamiltonian interactions. This allows one to perform holonomic quantum computing with these topological quantum computing systems. The tools we develop allow one to go beyond numerical simulations and understand these processes analytically.

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arXiv2013

Complex instruction set computing architecture for performing accurate quantum $Z$ rotations with less magic

We present quantum protocols for executing arbitrarily accurate $π/2^k$ rotations of a qubit about its $Z$ axis. Reduced instruction set computing (\textsc{risc}) architectures typically restrict the instruction set to stabilizer operations and a single non-stabilizer operation, such as preparation of a "magic" state from which $T = Z(π/4)$ gates can be teleported. Although the overhead required to distill high-fidelity copies of this magic state is high, the subsequent quantum compiling overhead to realize $Z$ rotations in a \textsc{risc} architecture can be much greater. We develop a complex instruction set computing (\textsc{cisc}) architecture whose instruction set includes stabilizer operations and preparation of magic states from which $Z(π/2^k)$ gates can be teleported, for $2 \leq k \leq k_{\text{max}}$. This results in a substantial overall reduction in the number of gates required to achieve a desired gate accuracy for $Z$ rotations. The key to our construction is a family of shortened quantum Reed-Muller codes of length $2^{k+2}-1$, whose magic-state distillation threshold shrinks with $k$ but is greater than 0.85% for $k \leq 6$.

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arXiv2011

Fault-tolerant quantum computing with color codes

We present and analyze protocols for fault-tolerant quantum computing using color codes. We present circuit-level schemes for extracting the error syndrome of these codes fault-tolerantly. We further present an integer-program-based decoding algorithm for identifying the most likely error given the syndrome. We simulated our syndrome extraction and decoding algorithms against three physically-motivated noise models using Monte Carlo methods, and used the simulations to estimate the corresponding accuracy thresholds for fault-tolerant quantum error correction. We also used a self-avoiding walk analysis to lower-bound the accuracy threshold for two of these noise models. We present and analyze two architectures for fault-tolerantly computing with these codes: one with 2D arrays of qubits are stacked atop each other and one in a single 2D substrate. Our analysis demonstrates that color codes perform slightly better than Kitaev's surface codes when circuit details are ignored. When these details are considered, we estimate that color codes achieve a threshold of 0.082(3)%, which is higher than the threshold of $1.3 \times 10^{-5}$ achieved by concatenated coding schemes restricted to nearest-neighbor gates in two dimensions but lower than the threshold of 0.75% to 1.1% reported for the Kitaev codes subject to the same restrictions. Finally, because the behavior of our decoder's performance for two of the noise models we consider maps onto an order-disorder phase transition in the three-body random-bond Ising model in 2D and the corresponding random-plaquette gauge model in 3D, our results also answer the Nishimori conjecture for these models in the negative: the statistical-mechanical classical spin systems associated to the 4.8.8 color codes are counterintuitively more ordered at positive temperature than at zero temperature.

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arXiv2011

Implications of Electronics Constraints for Solid-State Quantum Error Correction and Quantum Circuit Failure Probability

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 analyze one level of a quantum error correction circuit using nine data qubits in a Bacon-Shor code configured as a quantum memory. A hypothetical silicon double quantum dot quantum bit (qubit) is used as the fundamental element. A pessimistic estimate of the error probability of the quantum circuit is calculated using the total number of gates and idle time using a provably optimal schedule for the circuit operations obtained with an integer program methodology. The micro-architecture analysis provides insight about the different ways the electronics impact the circuit performance (e.g., extra idle time in the schedule), which can significantly limit the ultimate performance of any quantum circuit and therefore is a critical foundation for any future larger scale architecture analysis.

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arXiv2009

The impact of classical electronics constraints on a solid-state logical qubit memory

We describe a fault-tolerant memory for an error-corrected logical qubit based on silicon double quantum dot physical qubits. Our design accounts for constraints imposed by supporting classical electronics. A significant consequence of the constraints is to add error-prone idle steps for the physical qubits. Even using a schedule with provably minimum idle time, for our noise model and choice of error-correction code, we find that these additional idles negate any benefits of error correction. Using additional qubit operations, we can greatly suppress idle-induced errors, making error correction beneficial, provided the qubit operations achieve an error rate less than $2 \times 10^{-5}$. We discuss other consequences of these constraints such as error-correction code choice and physical qubit operation speed. While our analysis is specific to this memory architecture, the methods we develop are general enough to apply to other architectures as well.

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arXiv2008

Efficient feedback controllers for continuous-time quantum error correction

We present an efficient approach to continuous-time quantum error correction that extends the low-dimensional quantum filtering methodology developed by van Handel and Mabuchi [quant-ph/0511221 (2005)] to include error recovery operations in the form of real-time quantum feedback. We expect this paradigm to be useful for systems in which error recovery operations cannot be applied instantaneously. While we could not find an exact low-dimensional filter that combined both continuous syndrome measurement and a feedback Hamiltonian appropriate for error recovery, we developed an approximate reduced-dimensional model to do so. Simulations of the five-qubit code subjected to the symmetric depolarizing channel suggests that error correction based on our approximate filter performs essentially identically to correction based on an exact quantum dynamical model.

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arXiv2008

Universal quantum walks and adiabatic algorithms by 1D Hamiltonians

We construct a family of time-independent nearest-neighbor Hamiltonians coupling eight-state systems on a 1D ring that enables universal quantum computation. Hamiltonians in this family can achieve universality either by driving a continuous-time quantum walk or by terminating an adiabatic algorithm. In either case, the universality property can be understood as arising from an efficient simulation of a programmable quantum circuit. Using gadget perturbation theory, one can demonstrate the same kind of universality for related Hamiltonian families acting on qubits in 2D. Our results demonstrate that simulating 1D chains of spin-7/2 particles is BQP-hard, and indeed BQP-complete because the outputs of decision problems can be encoded in the outputs of such simulations.

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arXiv2006

Improved quantum algorithms for the ordered search problem via semidefinite programming

One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem using a constant factor fewer queries. However, the precise value of this constant is unknown. By characterizing a class of quantum query algorithms for ordered search in terms of a semidefinite program, we find new quantum algorithms for small instances of the ordered search problem. Extending these algorithms to arbitrarily large instances using recursion, we show that there is an exact quantum ordered search algorithm using 4 log_{605} N \approx 0.433 log_2 N queries, which improves upon the previously best known exact algorithm.

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