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Current technological advancements of quantum computers highlight the need for application-driven, practical and well-defined methods of benchmarking their performance. As the existing NISQ device's quality of two-qubit gate errors rate is…
Quantum compiling addresses the problem of approximating an arbitrary quantum gate with a string of gates drawn from a particular finite set. It has been shown that this is possible for almost all choices of base sets and furthermore that…
Concordant computation is a circuit-based model of quantum computation for mixed states, that assumes that all correlations within the register are discord-free (i.e. the correlations are essentially classical) at every step of the…
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
This study presents a roadmap towards utilizing a single arbitrary gate for universal quantum computing. Since two decades ago, it has been widely accepted that almost any single arbitrary gate with qubit number $>2$ is universal. Utilizing…
We theoretically consider possible errors in solid state quantum computation due to the interplay of the complex solid state environment and gate imperfections. In particular, we study two examples of gate operations in the opposite ends of…
A quantum position-verification scheme attempts to verify the spatial location of a prover. The prover is issued a challenge with quantum and classical inputs and must respond with appropriate timings. We consider two well-studied…
An essential element of classical computation is the "if-then" construct, that accepts a control bit and an arbitrary gate, and provides conditional execution of the gate depending on the value of the controlling bit. On the other hand,…
The Gottesman-Knill theorem asserts that a quantum circuit composed of Clifford gates can be efficiently simulated on a classical computer. Here we revisit this theorem and extend it to quantum circuits composed of Clifford and T gates,…
We consider recent works on the simulation of quantum circuits using the formalism of matrix product states and the formalism of contracting tensor networks. We provide simplified direct proofs of many of these results, extending an…
Loop is a powerful program construct in classical computation, but its power is still not exploited fully in quantum computation. The exploitation of such power definitely requires a deep understanding of the mechanism of quantum loop…
Quantum computing tries to exploit entanglement and interference to process information more efficiently than the best known classical solutions. Experiments demonstrating the feasibility of this approach have already been performed.…
The problem of distinguishing two unitary transformations, or quantum gates, is analyzed and a function reflecting their statistical distinguishability is found. Given two unitary operations, $U_1$ and $U_2$, it is proved that there always…
This course of lectures has been taught for several years at the Lomonosov Moscow State University; its modified version in 2021 is read in the Zhejiang University (Hangzhou), in the framework of summer school on quantum computing. The…
To guarantee the normal functioning of quantum devices in different scenarios, appropriate benchmarking tool kits are quite significant. Inspired by the recent progress on quantum state verification, here we establish a general framework of…
The so-called "threshold" theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum computation becomes feasible, even if all of the qubits involved are subject to relaxation processes,…
We study the class of two qubit gates which can be achieved using only linear optical elements (beam splitters and phase shifters) and post-selection. We are able to exactly characterize this set, and find that it is impossible to implement…
We use a random search technique to find quantum gate sequences that implement perfect quantum state preparation or unitary operator synthesis with arbitrary targets. This approach is based on the recent discovery that there is a large…
We present evidence that there exist quantum computations that can be carried out in constant depth, using 2-qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically…
We study the achievements of quantum circuits comprised of several one- and two-qubit gates. Quantum process matrices are determined for the basic one- and two-qubit gate operations and concatenated to yield the process matrix of the…