arXiv subjects

Natalie C. Brown

Publications and source records attributed to Natalie C. Brown.

12 recordsLinked to original sources

arXiv2026

Quantum Error-Corrected Computation of Molecular Energies

We present the first demonstration of an end-to-end pipeline with quantum error correction (QEC) for a quantum computation of the electronic structure of molecular systems. We calculate the ground-state energy of molecular hydrogen, using quantum phase estimation (QPE) on qubits encoded with the $[[7,1,3]]$ color code on Quantinuum H2--2. We obtain improvements in computational fidelity by (1) introducing several partially fault-tolerant (FT) techniques for the Clifford+$R_{Z}$ (arbitrary-angle single-qubit rotation) gate set, and (2) integrating Steane QEC gadgets for real-time error correction. In particular, the latter enhances the QPE circuits' performance despite the complexity of the extra QEC circuitry. The encoded circuits contain up to 1585 (546) fixed and 7202 (1702) conditional physical two-qubit gates (mid-circuit measurements), and $\sim$3900 ($\sim$760) total operations are applied on average. The energy $E$ is experimentally estimated to within $E - E_{\mathrm{FCI}} = 0.001(13)$ hartree, where $E_{\mathrm{FCI}}$ denotes the exact ground state energy within the given basis set. Additionally, we conduct numerical simulations with tunable noise parameters to identify the dominant sources of noise. We find that orienting the QEC protocols towards higher memory noise protection is the most promising avenue to improve our experimental results.

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arXiv2025

Controlled Gate Networks: Theory and Application to Eigenvalue Estimation

We introduce a new scheme for quantum circuit design called controlled gate networks. Rather than trying to reduce the complexity of individual unitary operations, the new strategy is to toggle between all of the unitary operations needed with the fewest number of gates. We present the general theory of controlled gate networks and show that, under quite general conditions, it can significantly reduce the number of two-qubit gates needed to produce linear combinations of unitary operators. The first example we consider is a variational subspace calculation for a two-qubit system. The second example is estimating the eigenvalues of a two-qubit Hamiltonian via the rodeo algorithm using operators that we call controlled reversal gates. We use the Quantinuum H1-2 and IBM Perth devices to realize the quantum circuits. The third example is the application of controlled gate networks to the controlled time evolution of a free nucleon on a three-dimensional lattice. For all of the examples, we show very substantial reductions in the number of two-qubit gates required. Our work demonstrates that controlled gate networks are a useful tool for reducing gate complexity in quantum algorithms for quantum many-body problems such as those relevant to nuclear physics.

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arXiv2025

Experimental Demonstration of High-Fidelity Logical Magic States from Code Switching

Preparation of high-fidelity logical magic states has remained as a necessary but daunting step towards building a large-scale fault-tolerant quantum computer. One approach is to fault-tolerantly prepare a magic state in one code and then switch to another, a method known as code switching. We experimentally demonstrate this protocol on an ion-trap quantum processor, yielding a logical magic state encoded in an error-correcting code with state-of-the-art logical fidelity. Our experiment is based on the first demonstration of code switching between color codes, from the fifteen-qubit quantum Reed-Muller code to the seven-qubit Steane code. We prepare an encoded magic state in the Steane code with $82.58\%$ probability, with an infidelity of at most $5.1(2.7) \times 10^{-4}$. The reported infidelity is lower than the leading infidelity of the physical operations utilized in the protocol by a factor of at least $2.7$, indicating the quantum processor is below the pseudo-threshold. Furthermore, we create two copies of the magic state in the same quantum processor and perform a logical Bell basis measurement for a sample-efficient certification of the encoded magic state. The high-fidelity magic state can be combined with the already-demonstrated fault-tolerant Clifford gates, state preparation, and measurement of the 2D color code, completing a universal set of fault-tolerant computational primitives with logical error rates equal or better than the physical two-qubit error rate.

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arXiv2024

Genons, Double Covers and Fault-tolerant Clifford Gates

A great deal of work has been done developing quantum codes with varying overhead and connectivity constraints. However, given the such an abundance of codes, there is a surprising shortage of fault-tolerant logical gates supported therein. We define a construction, such that given an input $[[n,k,d]]$ code, yields a $[[2n,2k,\ge d]]$ symplectic double code with naturally occurring fault-tolerant logical Clifford gates. As applied to 2-dimensional $D(\mathbb{Z}_2)$-topological codes with genons (twists) and domain walls, we find the symplectic double is genon free, and of possibly higher genus. Braiding of genons on the original code becomes Dehn twists on the symplectic double. Such topological operations are particularly suited for architectures with all-to-all connectivity, and we demonstrate this experimentally on Quantinuum's H1-1 trapped-ion quantum computer.

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arXiv2023

Advances in compilation for quantum hardware -- A demonstration of magic state distillation and repeat-until-success protocols

Fault-tolerant protocols enable large and precise quantum algorithms. Many such protocols rely on a feed-forward processing of data, enabled by a hybrid of quantum and classical logic. Representing the control structure of such programs can be a challenge. Here we explore two such fault-tolerant subroutines and analyze the performance of the subroutines using Quantum Intermediate Representation (QIR) as their underlying intermediate representation. First, we look at QIR's ability to leverage the LLVM compiler toolchain to unroll the quantum iteration logic required to perform magic state distillation on the $[[5,1,3]]$ quantum error-correcting code as originally introduced by Bravyi and Kitaev [Phys. Rev. A 71, 022316 (2005)]. This allows us to not only realize the first implementation of a real-time magic state distillation protocol on quantum hardware, but also demonstrate QIR's ability to optimize complex program structures without degrading machine performance. Next, we investigate a different fault-tolerant protocol that was first introduced by Paetznick and Svore [arXiv:1311.1074 (2013)], that reduces the amount of non-Clifford gates needed for a particular algorithm. We look at four different implementations of this two-stage repeat-until-success algorithm to analyze the performance changes as the results of programming choices. We find the QIR offers a viable representation for a compiled high-level program that performs nearly as well as a hand-optimized version written directly in quantum assembly. Both of these results demonstrate QIR's ability to accurately and efficiently expand the complexity of fault-tolerant protocols that can be realized today on quantum hardware.

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arXiv2022

Re-examining the quantum volume test: Ideal distributions, compiler optimizations, confidence intervals, and scalable resource estimations

The quantum volume test is a full-system benchmark for quantum computers that is sensitive to qubit number, fidelity, connectivity, and other quantities believed to be important in building useful devices. The test was designed to produce a single-number measure of a quantum computer's general capability, but a complete understanding of its limitations and operational meaning is still missing. We explore the quantum volume test to better understand its design aspects, sensitivity to errors, passing criteria, and what passing implies about a quantum computer. We elucidate some transient behaviors the test exhibits for small qubit number including the ideal measurement output distributions and the efficacy of common compiler optimizations. We then present an efficient algorithm for estimating the expected heavy output probability under different error models and compiler optimization options, which predicts performance goals for future systems. Additionally, we explore the original confidence interval construction and show that it underachieves the desired coverage level for single shot experiments and overachieves for more typical number of shots. We propose a new confidence interval construction that reaches the specified coverage for typical number of shots and is more efficient in the number of circuits needed to pass the test. We demonstrate these savings with a $QV=2^{10}$ experimental dataset collected from Quantinuum System Model H1-1. Finally, we discuss what the quantum volume test implies about a quantum computer's practical or operational abilities especially in terms of quantum error correction.

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arXiv2020

Resource-Efficient Quantum Computing by Breaking Abstractions

Building a quantum computer that surpasses the computational power of its classical counterpart is a great engineering challenge. Quantum software optimizations can provide an accelerated pathway to the first generation of quantum computing applications that might save years of engineering effort. Current quantum software stacks follow a layered approach similar to the stack of classical computers, which was designed to manage the complexity. In this review, we point out that greater efficiency of quantum computing systems can be achieved by breaking the abstractions between these layers. We review several works along this line, including two hardware-aware compilation optimizations that break the quantum Instruction Set Architecture (ISA) abstraction and two error-correction/information-processing schemes that break the qubit abstraction. Last, we discuss several possible future directions.

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arXiv2020

Critical faults of leakage errors on the surface code

Leakage is a particularly damaging error that occurs when a qubit leaves the defined computational subspace. Leakage errors limit the effectiveness of quantum error correcting codes by spreading additional errors to other qubits and corrupting syndrome measurements. The effects of leakage errors on the surface code has been studied in various contexts. However, the effects of a leaked data qubit versus a leaked ancilla qubit can be quite different. Here, we study the effects of data leakage and ancilla leakage separately. We show that data leakage is much less damaging. We show that the surface code maintains its distance in the presence of leakage by either confining leakage to data qubits or eliminating aniclla qubit leakage at the critical fault location. We also introduce new techniques for handling leakage by using gates with one-sided leakage and by mixing two types of leakage reducing circuits: one to handle data leakage and one to handle ancilla leakage.

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arXiv2019

Asymptotic Improvements to Quantum Circuits via Qutrits

Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qu$trits$. Past work with qutrits has demonstrated only constant factor improvements, owing to the $\log_2(3)$ binary-to-ternary compression factor. We present a novel technique using qutrits to achieve a logarithmic depth (runtime) decomposition of the Generalized Toffoli gate using no ancilla--a significant improvement over linear depth for the best qubit-only equivalent. Our circuit construction also features a 70x improvement in two-qudit gate count over the qubit-only equivalent decomposition. This results in circuit cost reductions for important algorithms like quantum neurons and Grover search. We develop an open-source circuit simulator for qutrits, along with realistic near-term noise models which account for the cost of operating qutrits. Simulation results for these noise models indicate over 90% mean reliability (fidelity) for our circuit construction, versus under 30% for the qubit-only baseline. These results suggest that qutrits offer a promising path towards scaling quantum computation.

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arXiv2019

Leakage mitigation for quantum error correction using a mixed qubit scheme

Leakage errors take qubits out of the computational subspace and will accumulate if not addressed. A leaked qubit will reduce the effectiveness of quantum error correction protocols due to the cost of implementing leakage reduction circuits and the harm caused by interacting leaked states with qubit states. Ion trap qubits driven by Raman gates have a natural choice between qubits encoded in magnetically insensitive hyperfine states that can leak and qubits encoded in magnetically sensitive Zeeman states of the electron spin that cannot leak. In our previous work, we compared these two qubits in the context of the toric code with a depolarizing leakage error model and found that for magnetic field noise with a standard deviation less than 32 $μ$G that the $^{174}$Yb$^+$ Zeeman qubit outperforms the $^{171}$Yb$^+$ hyperfine qubit. Here we examine a physically motivated leakage error model based on ions interacting via the Molmer-Sorenson gate. We find that this greatly improves the performance of hyperfine qubits but the Zeeman qubits are more effective for magnetic field noise with a standard deviation less than 10 $μ$G. At these low magnetic fields, we find that the best choice is a mixed qubit scheme where the hyperfine qubits are the ancilla and the leakage is handled without the need of an additional leakage reduction circuit.

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arXiv2019

Handling Leakage with Subsystem Codes

Leakage is a particularly damaging error that occurs when a qubit state falls out of its two-level computational subspace. Compared to independent depolarizing noise, leaked qubits may produce many more configurations of harmful correlated errors during error-correction. In this work, we investigate different local codes in the low-error regime of a leakage gate error model. When restricting to bare-ancilla extraction, we observe that subsystem codes are good candidates for handling leakage, as their locality can limit damaging correlated errors. As a case study, we compare subspace surface codes to the subsystem surface codes introduced by Bravyi et al. In contrast to depolarizing noise, subsystem surface codes outperform same-distance subspace surface codes below error rates as high as $\lessapprox 7.5 \times 10^{-4}$ while offering better per-qubit distance protection. Furthermore, we show that at low to intermediate distances, Bacon-Shor codes offer better per-qubit error protection against leakage in an ion-trap motivated error model below error rates as high as $\lessapprox 1.2 \times 10^{-3}$. For restricted leakage models, this advantage can be extended to higher distances by relaxing to unverified two-qubit cat state extraction in the surface code. These results highlight an intrinsic benefit of subsystem code locality to error-corrective performance.

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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.

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