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Many quantum states arising in algorithms and physical systems occupy only a small, structured subset of the exponentially large Hilbert space, yet standard quantum state tomography fails to exploit this structure. We present an efficient…
The quantum Fourier transform and quantum wavelet transform have been cornerstones of quantum information processing. However, for non-stationary signals and anomaly detection, the Hilbert transform can be a more powerful tool, yet no prior…
The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…
We apply a hybrid evolutionary algorithm to minimize the depth of circuits in quantum computing. More specifically, we evaluate two different variants of the algorithm. In the first approach, we combine the evolutionary algorithm with an…
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…
Constrained combinatorial optimization with strict linear constraints underpins applications in drug discovery, power grids, logistics, and finance, yet remains computationally demanding for classical algorithms, especially at large scales.…
Qubit-based variational quantum algorithms have undergone rapid development in recent years but still face several challenges. In this context, we propose a symmetry-enhanced digitized counterdiabatic quantum algorithm utilizing qudits…
Preparing the ground state of a local Hamiltonian is a crucial problem in understanding quantum many-body systems, with applications in a variety of physics fields and connections to combinatorial optimization. While various quantum…
In quantum estimation for a $d$-parameter family of density operators on a finite-dimensional Hilbert space $\mathcal{H}$, an estimator is specified by a pair $\left(M,\hat{\theta}\right)$, where $M$ is a POVM with a finite outcome set…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
Quantum ptychography is a method for estimating an unknown pure quantum state by subjecting it to overlapping projections, each one followed by a projective measurement on a single prescribed basis. Here, we present a comprehensive study of…
Quantum weight reduction is the task of transforming a quantum code with large check weight into one with small check weight. Low-weight codes are essential for implementing quantum error correction on physical hardware, since high-weight…
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
In contexts where relevant problems can easily attain configuration spaces of enormous sizes, solving Linear Differential Equations (LDEs) can become a hard achievement for classical computers; on the other hand, the rise of quantum…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
There exist numerous problems in nature inherently described by finite $D$-dimensional states. Formulating these problems for execution on qubit-based quantum hardware requires mapping the qudit Hilbert space to that of multiqubit which may…
Quantum multiparameter estimation offers a framework for the simultaneous estimation of multiple parameters, pertaining to possibly noncommutating observables. While the optimal probe for estimating a single unitary phase is well understood…
We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use…
We consider a protocol to perform the optimal quantum state discrimination of $N$ linearly independent non-orthogonal pure quantum states and present a computational code. Through the extension of the original Hilbert space, it is possible…
This work outlines a consistent method of identifying subsystems in finite-dimensional Hilbert spaces, independent of the underlying inner-product structure. Such Hilbert spaces arise in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics,…