arXiv subjects

Margarite L. LaBorde

Publications and source records attributed to Margarite L. LaBorde.

15 recordsLinked to original sources

arXiv2026

Satisfying Quantum Codes: Physics-Informed and Hardware-Aware Code Design with SAT Solvers

Although quantum error correction is widely believed to be necessary for impactful applications of quantum computers, the design of quantum error correction codes is largely done by hand, without respect to problem or hardware constraints. In this work, we present a highly general and flexible framework for the computational design of both physics-inspired and hardware-aware quantum codes. To do so, we formulate code design as a Boolean satisfiability (SAT) problem and show how to incorporate all required error correction criteria. We prove that code design is NP-complete, ruling out any efficient algorithm for designing codes in general. Nonetheless, we show that state-of-the-art SAT solvers are able to effectively find solutions for many practical problems. Notably, we are able to design physics-inspired codes with up to 100 physical qubits in minutes, and we design new hardware-aware codes for biased noise which have a lower logical error rate than state-of-the-art surface codes.

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arXiv2026

Symmetry-Based Quantum Codes Beyond the Pauli Group

Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that allows the code designer to take this structure into account. For any representation of a finite group, we produce a quantum code with a code space invariant under the group action, providing passive error mitigation against errors belonging to the image of the representation. Furthermore, errors outside this scope are detected and diagnosed by performing a projective measurement onto the isotypic components corresponding to irreducible representations of the chosen group, effectively generalizing syndrome extraction to symmetry-resolved quantum measurements. We show that all stabilizer codes are a special case of this construction, including qudit stabilizer codes, and show that there is a natural one logical qubit code associated to the dihedral group. Thus we provide a unifying framework for existing codes while simultaneously facilitating symmetry-aware codes tailored to specific systems.

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arXiv2025

A Closed Form for Moment-Based Entanglement Tests Associated to the PPT Criterion

Neven et al. have explored an unexpected alliance between the mathematical insights of Sir Isaac Newton and René Descartes which culminates in the reduction of the Positive Partial Transpose (PPT) criterion to an equivalent hierarchy of entanglement tests based on the moments of the partial transpose. By repurposing these classical results in the context of modern quantum theory, they illuminate new pathways for entanglement verification. Here, we expand on this work by providing a closed form for the inequalities defining these entanglement tests and producing an equivalent set of graph theoretic conditions on the weighted graph induced by the partial transpose.

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arXiv2025

Learning Equivariant Maps with Variational Quantum Circuits

Geometric quantum machine learning uses the symmetries inherent in data to design tailored machine learning tasks with reduced search space dimension. The field has been well-studied recently in an effort to avoid barren plateau issues while improving the accuracy of quantum machine learning models. This work explores the related problem of learning an equivariant map given two unitary representations of a finite group, which in turn allows the symmetric embedding of the data to be learned rather than simply required. Moreover, this procedure allows the learning of covariant quantum channels, which are an essential tool in quantum information theory. We demonstrate the feasibility of this task and give examples to illustrate the procedure.

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arXiv2025

Learning with SASQuaTCh: a Novel Variational Quantum Transformer Architecture with Kernel-Based Self-Attention

The recent exploding growth in size of state-of-the-art machine learning models highlights a well-known issue where exponential parameter growth, which has grown to trillions as in the case of the Generative Pre-trained Transformer (GPT), leads to training time and memory requirements which limit their advancement in the near term. The predominant models use the so-called transformer network and have a large field of applicability, including predicting text and images, classification, and even predicting solutions to the dynamics of physical systems. Here we present a variational quantum circuit architecture named Self-Attention Sequential Quantum Transformer Channel (SASQuaTCh), which builds networks of qubits that perform analogous operations of the transformer network, namely the keystone self-attention operation, and leads to an exponential improvement in parameter complexity and run-time complexity over its classical counterpart. Our approach leverages recent insights from kernel-based operator learning in the context of predicting spatiotemporal systems to represent deep layers of a vision transformer network using simple gate operations and a set of multi-dimensional quantum Fourier transforms. To validate our approach, we consider image classification tasks in simulation and with hardware, where with only 9 qubits and a handful of parameters we are able to simultaneously embed and classify a grayscale image of handwritten digits with high accuracy.

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arXiv2025

Quantum Computational Complexity and Symmetry

Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the difficulty of symmetry-testing problems involving a unitary representation of a group and a state or a channel that is being tested. In particular, we prove that various such symmetry-testing problems are complete for BQP, QMA, QSZK, QIP(2), QIP_EB(2), and QIP, thus spanning the prominent classes of the quantum interactive proof hierarchy and forging a non-trivial connection between symmetry and quantum computational complexity. Finally, we prove the inclusion of two Hamiltonian symmetry-testing problems in QMA and QAM, while leaving it as an intriguing open question to determine whether these problems are complete for these classes.

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arXiv2024

Logarithmic-Depth Quantum Circuits for Hamming Weight Projections

A pure state of fixed Hamming weight is a superposition of computational basis states such that each bitstring in the superposition has the same number of ones. Given a Hilbert space of the form $\mathcal{H} = (\mathbb{C}_2)^{\otimes n}$, or an $n$-qubit system, the identity operator can be decomposed as a sum of projectors onto subspaces of fixed Hamming weight. In this work, we propose several quantum algorithms that realize a coherent Hamming weight projective measurement on an input pure state, meaning that the post-measurement state of the algorithm is the projection of the input state onto the corresponding subspace of fixed Hamming weight. We analyze a depth-width trade-off for the corresponding quantum circuits, allowing for a depth reduction of the circuits at the cost of more control qubits. For an $n$-qubit input, the depth-optimal algorithm uses $O(n)$ control qubits and the corresponding circuit has depth $O(\log (n))$, assuming that we have the ability to perform qubit resets. Furthermore, the proposed algorithm construction uses only one- and two-qubit gates.

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arXiv2024

Quantum Algorithms for Realizing Symmetric, Asymmetric, and Antisymmetric Projectors

In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning applications, and certain asymmetric quantum states are known to be resourceful in various applications. Symmetry testing algorithms provide a means to identify and quantify these properties with respect to a representation of a group. In this paper, we present a collection of quantum algorithms that realize projections onto the symmetric subspace, as well as the asymmetric subspace, of quantum systems. We describe how this can be modified to realize an antisymmetric projection as well, and we show how projectors can be combined in a systematic way to effectively measure various projections in a single quantum circuit. Using these constructions, we demonstrate applications such as testing for Werner-state symmetry and estimating Schmidt ranks of bipartite states, supported by experimental data from IBM Quantum systems. This work underscores the pivotal role of symmetry in simplifying quantum calculations and advancing quantum information tasks.

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arXiv2024

Cycle Index Polynomials and Generalized Quantum Separability Tests

The mixedness of one share of a pure bipartite state determines whether the overall state is a separable, unentangled state. Here we consider quantum computational tests of mixedness, and we derive an exact expression of the acceptance probability of such tests as the number of copies of the state becomes larger. We prove that the analytical form of this expression is given by the cycle index polynomial of the symmetric group $S_k$, which is itself related to the Bell polynomials. After doing so, we derive a family of quantum separability tests, each of which is generated by a finite group; for all such algorithms, we show that the acceptance probability is determined by the cycle index polynomial of the group. Finally, we produce and analyze explicit circuit constructions for these tests, showing that the tests corresponding to the symmetric and cyclic groups can be executed with $O(k^2)$ and $O(k\log(k))$ controlled-SWAP gates, respectively, where $k$ is the number of copies of the state being tested.

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arXiv2023

Quantum Algorithms for Testing Hamiltonian Symmetry

Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian exhibits symmetry with respect to a group. We demonstrate that familiar expressions of Hamiltonian symmetry in quantum mechanics correspond directly with the acceptance probabilities of our algorithms. We execute one of our symmetry-testing algorithms on existing quantum computers for simple examples of both symmetric and asymmetric cases.

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arXiv2023

Testing symmetry on quantum computers

Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian realizing a time evolution are not useful for timekeeping during that evolution, and bipartite states that are highly extendible are not strongly entangled and thus not useful for basic tasks like teleportation. Motivated by this perspective, this paper details several quantum algorithms that test the symmetry of quantum states and channels. For the case of testing Bose symmetry of a state, we show that there is a simple and efficient quantum algorithm, while the tests for other kinds of symmetry rely on the aid of a quantum prover. We prove that the acceptance probability of each algorithm is equal to the maximum symmetric fidelity of the state being tested, thus giving a firm operational meaning to these latter resource quantifiers. Special cases of the algorithms test for incoherence or separability of quantum states. We evaluate the performance of these algorithms on choice examples by using the variational approach to quantum algorithms, replacing the quantum prover with a parameterized circuit. We demonstrate this approach for numerous examples using the IBM quantum noiseless and noisy simulators, and we observe that the algorithms perform well in the noiseless case and exhibit noise resilience in the noisy case. We also show that the maximum symmetric fidelities can be calculated by semi-definite programs, which is useful for benchmarking the performance of these algorithms for sufficiently small examples. Finally, we establish various generalizations of the resource theory of asymmetry, with the upshot being that the acceptance probabilities of the algorithms are resource monotones and thus well motivated from the resource-theoretic perspective.

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arXiv2023

Quantum Entanglement & Purity Testing: A Graph Zeta Function Perspective

We assign an arbitrary density matrix to a weighted graph and associate to it a graph zeta function that is both a generalization of the Ihara zeta function and a special case of the edge zeta function. We show that a recently developed bipartite pure state separability algorithm based on the symmetric group is equivalent to the condition that the coefficients in the exponential expansion of this zeta function are unity. Moreover, there is a one-to-one correspondence between the nonzero eigenvalues of a density matrix and the singularities of its zeta function. Several examples are given to illustrate these findings.

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arXiv2023

A Menagerie of Symmetry Testing Quantum Algorithms

This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We begin by establishing the necessary mathematical background. We show how to generate a notion of symmetry from a discrete, finite group and how this generalizes to a continuous group. We then use these notions to investigate Hamiltonian symmetries. We propose quantum algorithms capable of testing whether a Hamiltonian exhibits symmetry with respect to a group and show that this algorithm is DQC1-Complete. We next discuss tests of symmetry for quantum states. We prove that the acceptance probability of each algorithm is equal to the maximum symmetric fidelity of the state being tested and establish various generalizations of the resource theory of asymmetry. In the next chapter, we show that the analytical form of the acceptance probability of such a test is given by the cycle index polynomial of the symmetric group $S_k$. We derive a family of quantum separability tests, each of which is generated by a finite group; for all such algorithms, we show that the acceptance probability is determined by the cycle index polynomial of the group. Finally, we produce and analyze explicit circuit constructions for these tests, showing that the tests corresponding to the symmetric and cyclic groups can be executed with $O(k^2)$ and $O(k\log(k))$ controlled-SWAP gates, respectively, where $k$ is the number of copies of the state. Finally, we include additional results not previously published; specifically, we give a test for symmetry of a quantum state using density matrix exponentiation, a further result of Hamiltonian symmetry measurements when using Abelian groups, and an alternate Hamiltonian symmetry test construction for a block-encoded Hamiltonian.

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arXiv2020

Finding Broken Gates in Quantum Circuits---Exploiting Hybrid Machine Learning

Current implementations of quantum logic gates can be highly faulty and introduce errors. In order to correct these errors, it is necessary to first identify the faulty gates. We demonstrate a procedure to diagnose where gate faults occur in a circuit by using a hybridized quantum-and-classical K-Nearest-Neighbors (KNN) machine-learning technique. We accomplish this task using a diagnostic circuit and selected input qubits to obtain the fidelity between a set of output states and reference states. The outcomes of the circuit can then be stored to be used for a classical KNN algorithm. We numerically demonstrate an ability to locate a faulty gate in circuits with over 30 gates and up to nine qubits with over 90% accuracy.

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arXiv2017

Multiparameter estimation with single photons

It was suggested in Ref. [Phys. Rev. Lett. 114, 170802] that optical networks with relatively inexpensive overhead---single photon Fock states, passive optical elements, and single photon detection---can show significant improvements over classical strategies for single-parameter estimation, when the number of modes in the network is small (n < 7). A similar case was made in Ref. [Phys. Rev. Lett. 111, 070403] for multi-parameter estimation, where measurement is instead made using photon-number resolving detectors. In this paper, we analytically compute the quantum Cramér-Rao bound to show these networks can have a constant-factor quantum advantage in multi-parameter estimation for even large number of modes. Additionally, we provide a simplified measurement scheme using only single-photon (on-off) detectors that is capable of approximately obtaining this sensitivity for a small number of modes.

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