Related papers: Quantum encoder for fixed Hamming-weight subspaces
Quantum computers are a revolutionary class of computational platforms with applications in combinatorial and global optimization, machine learning, and other domains involving computationally hard problems. While these machines typically…
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 $\mathcal{H} = (\mathbb{C}_2)^{\otimes n}$,…
Quantum noise in real-world devices poses a significant challenge in achieving practical quantum advantage, since accurately compiled and executed circuits are typically deep and highly susceptible to decoherence. To facilitate the…
Transversal gates are logical gate operations on encoded quantum information that are efficient in gate count and depth, and are designed to minimize error propagation. Efficient encoding circuits for quantum codes that admit transversal…
Loading functions into quantum computers represents an essential step in several quantum algorithms, such as quantum partial differential equation solvers. Therefore, the inefficiency of this process leads to a major bottleneck for the…
Quantum state preparation, also known as encoding or embedding, is a crucial initial step in many quantum algorithms and often constrains theoretical quantum speedup in fields such as quantum machine learning and linear equation solvers.…
The stable operation of quantum computers will rely on error-correction, in which single quantum bits of information are stored redundantly in the Hilbert space of a larger system. Such encoded qubits are commonly based on arrays of many…
Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications,…
Gate-based universal quantum computation is formulated in terms of two types of operations: local single-qubit gates, which are typically easily implementable, and two-qubit entangling gates, whose faithful implementation remains one of the…
We introduce a framework for simulating hybrid oscillator-qubit quantum processors on qubit-only systems through position encoding. By encoding continuous-variable position and momentum wave functions into qubit amplitudes, our method…
The amplitude encoding of an arbitrary $n$-qubit state vector requires $\Omega(2^n)$ gate operations, owing to the exponential dimension of the Hilbert space. We can, however, form dimensionality-reduced representations of quantum states…
The weighted MAX k-CUT problem involves partitioning a weighted undirected graph into k subsets, or colors, to maximize the sum of the weights of edges between vertices in different subsets. This problem has significant applications across…
We construct a fault-tolerant quantum error-correcting protocol based on a qubit encoded in a large spin qudit using a spin-cat code, analogous to the continuous variable cat encoding. With this, we can correct the dominant error sources,…
Hybrid variational quantum algorithms (VQAs) are promising for solving practical problems such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers.…
Encoding in a high-dimensional Hilbert space improves noise resilience in quantum information processing. This approach, however, may result in cross-mode coupling and detection complexities, thereby reducing quantum cryptography…
The weighted MAX k-CUT problem consists of finding a k-partition of a given weighted undirected graph G(V,E) such that the sum of the weights of the crossing edges is maximized. The problem is of particular interest as it has a multitude of…
As we continue to find applications where the currently available noisy devices exhibit an advantage over their classical counterparts, the efficient use of quantum resources is highly desirable. The notion of quantum autoencoders was…
Hybrid variational quantum algorithms are promising for solving practical problems, such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers.…
Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing…
Quantum hashing is a useful technique that allows us to construct memory-efficient algorithms and secure quantum protocols. First, we present a circuit that implements the phase form of quantum hashing using $2^{n-1}$ CNOT gates, where n is…