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The expressibility and trainability of parameterized quantum circuits has been shown to be intimately related to their associated dynamical Lie algebras (DLAs). From a quantum algorithm design perspective, given a set $A$ of DLA generators,…
Variational quantum algorithms (VQAs) have emerged as the leading strategy to obtain quantum advantage on the current noisy intermediate-scale devices. However, their entanglement-trainability correlation, as the major reason for the barren…
Exploiting the power of quantum computation to realise superior machine learning algorithmshas been a major research focus of recent years, but the prospects of quantum machine learning (QML) remain dampened by considerable technical…
The performance of the Quantum Approximate Optimization Algorithm (QAOA) is closely tied to the structure of the dynamical Lie algebra (DLA) generated by its Hamiltonians, which determines both its expressivity and trainability. In this…
In this paper, we investigate the performances of tunable quantum neural networks in the Quantum Probably Approximately Correct (QPAC) learning framework. Tunable neural networks are quantum circuits made of multi-controlled X gates. By…
The XY-mixer has widespread utilization in modern quantum computing, including in variational quantum algorithms, such as Quantum Alternating Operator Ansatz (QAOA). The XY ansatz is particularly useful for solving Cardinality Constrained…
$\bf{Abstract}$: A qubit lattice algorithm (QLA), which consists of a set of interleaved unitary collision-streaming operators, is developed for electromagnetic wave propagation in tensor dielectric media. External potential operators are…
The quest for successful variational quantum machine learning (QML) relies on the design of suitable parametrized quantum circuits (PQCs), as analogues to neural networks in classical machine learning. Successful QML models must fulfill the…
We find an application in quantum finite automata for the ideas and results of [JL21] and [JL22]. We reformulate quantum finite automata with multiple-time measurements using the algebraic notion of near-ring. This gives a unified…
Quantum Machine Learning (QML) is considered to be one of the most promising applications of near term quantum devices. However, the optimization of quantum machine learning models presents numerous challenges arising from the imperfections…
Certain types of quantum computing platforms, such as those realized using Rydberg atoms or Kerr-cat qubits, are natively more susceptible to Pauli-Z noise than Pauli-X noise, or vice versa. On such hardware, it is useful to ensure that…
Variational algorithms such as the Quantum Approximate Optimization Algorithm have attracted attention due to their potential for solving problems using near-term quantum computers. The $ZZ$ interaction typically generates the primitive…
Dynamical Lie algebras (DLAs) have emerged as a valuable tool in the study of parameterized quantum circuits, helping to characterize both their expressiveness and trainability. In particular, the absence or presence of barren plateaus…
In the current noisy intermediate-scale quantum (NISQ) era, quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. In quantum machine learning, the gates of a quantum circuit are parametrized,…
Determining the physically accessible unitary dynamics of a quantum system under finite Hamiltonian resources is a central problem in quantum control and Hamiltonian engineering. Dynamical Lie algebras (DLAs) provide the fundamental link…
Quantum computing has promised significant improvement in solving difficult computational tasks over classical computers. Designing quantum circuits for practical use, however, is not a trivial objective and requires expert-level knowledge.…
The design and optimization of realistic architectures for fault-tolerant quantum computation requires error models that are both reliable and amenable to large-scale classical simulation. Perhaps the simplest and most practical…
Quantum machine learning (QML) has been identified as one of the key fields that could reap advantages from near-term quantum devices, next to optimization and quantum chemistry. Research in this area has focused primarily on variational…
We propose a quantum machine learning framework for estimating classical covariance matrices using parameterized quantum circuits within the Pauli-Correlation-Encoding (PCE) paradigm. We introduce two quantum covariance estimators: the…
Superconducting qubits are a promising candidate for building a quantum computer. A continued challenge for fast yet accurate gates to minimize the effects of decoherence. Here we apply numerical methods to design fast entangling gates,…