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In this work, we report on a novel quantum state reconstruction process based on the disentanglement algorithm. Using variational quantum circuits, we disentangle the quantum state to a product of computational zero states. Inverse…
For the preparation of high-dimensional functions on quantum computers, we introduce tensor network algorithms that are efficient with regard to dimensionality, optimize circuits composed of hardware-native gates and take gate errors into…
Quantum state tomography (QST) is plagued by the ``curse of dimensionality'' due to the exponentially-scaled complexity in measurement and data post-processing. Efficient QST schemes for large-scale mixed states are currently missing. In…
In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that…
Entanglement among a large number of qubits is a crucial resource for many quantum algorithms. Such many-body states have been efficiently generated by entangling a chain of itinerant photonic qubits in the optical or microwave domain.…
Logistic regression (LR) is an important machine learning model for classification, with wide applications in text classification, image analysis and medicine diagnosis, etc. However, training LR generally entails an iterative gradient…
Characterizing complex quantum systems is a vital task in quantum information science. Quantum tomography, the standard tool used for this purpose, uses a well-designed measurement record to reconstruct quantum states and processes. It is,…
We consider the rank minimization problem from quadratic measurements, i.e., recovering a rank $r$ matrix $X \in \mathbb{R}^{n \times r}$ from $m$ scalar measurements $y_i=a_i^{\top} XX^{\top} a_i,\;a_i\in \mathbb{R}^n,\;i=1,\ldots,m$. Such…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
The estimation of high dimensional quantum states is an important statistical problem arising in current quantum technology applications. A key example is the tomography of multiple ions states, employed in the validation of state…
We propose efficient algorithms with logarithmic step complexities for the generation of entangled $GHZ_N$ and $W_N$ states useful for quantum networks, and we demonstrate an implementation on the IBM quantum computer up to $N=16$. Improved…
We study the projected gradient descent method on low-rank matrix problems with a strongly convex objective. We use the Burer-Monteiro factorization approach to implicitly enforce low-rankness; such factorization introduces non-convexity in…
Classical computation of electronic properties in large-scale materials remains challenging. Quantum computation has the potential to offer advantages in memory footprint and computational scaling. However, general and practical quantum…
Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that…
Computing the ground state of interacting quantum matter is a long-standing challenge, especially for complex two-dimensional systems. Recent developments have highlighted the potential of neural quantum states to solve the quantum…
Quantum State Tomography is the task of determining an unknown quantum state by making measurements on identical copies of the state. Current algorithms are costly both on the experimental front -- requiring vast numbers of measurements --…
Block encoding is a key ingredient in the recently developed quantum singular value transformation (QSVT) framework, which provides a unifying description for many quantum algorithms. Initially introduced to simplify and optimize resource…
Image-based data is a popular arena for testing quantum machine learning algorithms. A crucial factor in realizing quantum advantage for these applications is the ability to efficiently represent images as quantum states. Here we present a…
We consider a generic framework of optimization algorithms based on gradient descent. We develop a quantum algorithm that computes the gradient of a multi-variate real-valued function $f:\mathbb{R}^d\rightarrow \mathbb{R}$ by evaluating it…
Density Matrix Renormalization Group (DMRG) algorithm has been extremely successful for computing the ground states of one-dimensional quantum many-body systems. For problems concerned with mixed quantum states, however, it is less…