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Quantum circuits with local particle number conservation (LPNC) restrict the quantum computation to a subspace of the Hilbert space of the qubit register. In a noiseless or fault-tolerant quantum computation, such quantities are preserved.…
Foundation models are highly versatile neural-network architectures capable of processing different data types, such as text and images, and generalizing across various tasks like classification and generation. Inspired by this success, we…
The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the nontrivial correlations encoded in the many-body wave functions with high complexity. Quantum neural network provides a…
Simulating the dynamics of electrons and other fermionic particles in quantum chemistry, materials science, and high-energy physics is one of the most promising applications of fault-tolerant quantum computers. However, the overhead in…
We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…
Measurement correlations in quantum systems can exhibit non-local behavior, a fundamental aspect of quantum mechanics with applications such as device-independent quantum information processing. However, the explicit construction of local…
We show, for the first time, that continuous dynamical decoupling can preserve the coherence of a two-qubit state as it evolves during a SWAP quantum operation. Hence, because the Heisenberg exchange interaction alone can be used for…
Transport phenomena play a key role in a variety of application domains, and efficient simulation of these dynamics remains an outstanding challenge. While quantum computers offer potential for significant speedups, existing algorithms…
Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is…
Accurate amine property prediction is essential for optimizing CO2 capture efficiency in post-combustion processes. Quantum machine learning (QML) can enhance predictive modeling by leveraging superposition, entanglement, and interference…
This thesis explores the application of the Symmetry-Breaking/Symmetry-Restoration methodology on quantum computers to better approximate a Hamiltonian's ground state energy within a variational framework in many-body physics. This involves…
Quantum computers potentially have an exponential advantage over classical computers for the quantum simulation of many-fermion quantum systems. Nonetheless, fermions are more expensive to simulate than bosons due to the fermionic encoding…
Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic…
Quantum computing has the potential to revolutionize quantum chemistry and material science by offering solutions to complex problems unattainable with classical computers. However, the development of efficient quantum algorithms that are…
Neighborhood Preserving Embedding (NPE) is an important linear dimensionality reduction technique that aims at preserving the local manifold structure. NPE contains three steps, i.e., finding the nearest neighbors of each data point,…
In this paper the entanglement of multi-qubit fermionic pseudo Hermitian coherent states (FPHCS) described by anticommutative Grassmann numbers is studied. The pseudo-Hermitian versions of the well known maximally entangled pure states such…
Noisy intermediate-scale quantum (NISQ) computers could solve quantum-mechanical simulation problems that are beyond the capabilities of classical computers. However, NISQ devices experience significant errors which, if not corrected, can…
We review analyses of open quantum systems. We show how non-Hermiticity arises in an open quantum system with an infinite environment, focusing on the one-body problem. One of the reasons for taking the present approach is that we can solve…
Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite lifetime. Hybrid algorithms leveraging classical resources have demonstrated promising initial results…