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Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…
Iterates of quantum operations and their convergence are investigated in the context of mean ergodic theory. We discuss in detail the convergence of the iterates and show that the uniform ergodic theorem plays an essential role. Our results…
One-way measurement based quantum computations (1WQC) may describe unitary transformations, via a composition of CPTP maps which are not all unitary themselves. This motivates the following decision problems: Is it possible to determine…
Johnson-Lindenstrauss embeddings are widely used to reduce the dimension and thus the processing time of data. To reduce the total complexity, also fast algorithms for applying these embeddings are necessary. To date, such fast algorithms…
Qubit-resolved operations and measurements are required for most current quantum information processing schemes. However, these operations can be experimentally costly due to the need for local addressing, demanding significant classical…
We consider the problem of estimating multiple analytic functions of a set of local parameters via qubit sensors in a quantum sensor network. To address this problem, we highlight a generalization of the sensor symmetric performance bounds…
In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning…
The precision of quantum metrology is widely believed to be restricted by the Heisenberg limit, corresponding to a root mean square error that is inversely proportional to the number of independent processes probed in an experiment, N. In…
As Noisy Intermediate-Scale Quantum (NISQ) devices grow in number of qubits, determining good or even adequate parameter configurations for a given application, or for device calibration, becomes a cumbersome task. An evolutionary algorithm…
We propose a quantum machine learning algorithm for efficiently solving a class of problems encoded in quantum controlled unitary operations. The central physical mechanism of the protocol is the iteration of a quantum time-delayed equation…
Unitary operation is an essential step for quantum information processing. We first propose an iterative procedure for decomposing a general unitary operation without resorting to controlled-NOT gate and single-qubit rotation library. Based…
An important result in the theory of quantum control is the "universality" of $2$-local unitary gates, i.e. the fact that any global unitary evolution of a system of $L$ qudits can be implemented by composition of $2$-local unitary gates.…
Unitary $k$-designs are distributions of unitary gates that match the Haar distribution up to its $k$-th statistical moment. They are a crucial resource for randomized quantum protocols. However, their implementation on encoded logical…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
Twist-untwist protocols for quantum metrology consist of a serial application of: 1. unitary nonlinear dynamics (e.g., spin squeezing or Kerr nonlinearity), 2. parameterized dynamics $U(\phi)$ (e.g., a collective rotation or phase space…
The impossibility of deterministic and error-free discrimination among nonorthogonal quantum states lies at the core of quantum theory and constitutes a primitive for secure quantum communication. Demanding determinism leads to errors,…
We address the problem of exact and approximate transformation of quantum dichotomies in the asymptotic regime, i.e., the existence of a quantum channel $\mathcal E$ mapping $\rho_1^{\otimes n}$ into $\rho_2^{\otimes R_nn}$ with an error…
Simulating quantum systems with their environments often requires non-unitary operations, and mapping these to quantum devices often involves expensive dilations or prohibitive measurement costs to achieve desired precisions. Building on…
This thesis reports advances in the theory of design, characterization and simulation of multi-photon multi-channel interferometers. I advance the design of interferometers through an algorithm to realize an arbitrary discrete unitary…
One of the most challenging problems for the realization of a scalable quantum computer is to design a physical device that keeps the error rate for each quantum processing operation low. These errors can originate from the accuracy of…