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We prove that constant-depth quantum circuits are more powerful than their classical counterparts. To this end we introduce a non-oracular version of the Bernstein-Vazirani problem which we call the 2D Hidden Linear Function problem. An…
In this paper we introduce a technique and a tool for formal verification of various quantum information processing protocols. The tool uses stabilizer formalism and is capable of representing concurrent quantum protocol, thus is more…
As the size and complexity of a quantum computer increases, quantum bit (qubit) characterization and gate optimization become complex and time-consuming tasks. Current calibration techniques require complicated and verbose measurements to…
The study of classical algorithms is supported by an immense understructure, founded in logic, type, and category theory, that allows an algorithmist to reason about the sequential manipulation of data irrespective of a computation's…
Using electrostatic gates to control the electron positions, we present a new controlled-NOT gate based on quantum dots. The qubit states are chosen to be the spin states of an excess conductor electron in the quantum dot; and the main…
Existing quantum compilers optimize quantum circuits by applying circuit transformations designed by experts. This approach requires significant manual effort to design and implement circuit transformations for different quantum devices,…
We present new optimal and heuristic algorithms for exact synthesis of multi-qubit unitaries and isometries. For example, our algorithms find Clifford and T circuits for unitaries with entries in $\mathbb{Z}[i,1/\sqrt{2}]$. The optimal…
We present a quantum circuit optimization technique that takes into account the variability in error rates that is inherent across present day noisy quantum computing platforms. This method can be run post qubit routing or post-compilation,…
As the width and depth of quantum circuits implemented by state-of-the-art quantum processors rapidly increase, circuit analysis and assessment via classical simulation are becoming unfeasible. It is crucial, therefore, to develop new…
Implementing many important sub-circuits on near-term quantum devices remains a challenge due to the high levels of noise and the prohibitive depth on standard nearest-neighbour topologies. Overcoming these barriers will likely require…
The Fourier expansion of the loss function in variational quantum algorithms (VQA) contains a wealth of information, yet is generally hard to access. We focus on the class of variational circuits, where constant gates are Clifford gates and…
In recent years qubit designs such as transmons approached the fidelities of up to 0.999. However, even these devices are still insufficient for realizing quantum error correction requiring better than 0.9999 fidelity. Topologically…
The gauge field formalism, or operator-valued cochain formalism, has recently emerged as a powerful framework for describing quantum Calderbank-Shor-Steane (CSS) codes. In this work, we extend this framework to construct a broad class of…
Quantum compiling, a process that decomposes the quantum algorithm into a series of hardware-compatible commands or elementary gates, is of fundamental importance for quantum computing. We introduce an efficient algorithm based on deep…
Before executing a quantum algorithm, one must first decompose the algorithm into machine-level instructions compatible with the architecture of the quantum computer, a process known as quantum compiling. There are many different quantum…
The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
This work presents a precise connection between Clifford circuits, Shor's factoring algorithm and several other famous quantum algorithms with exponential quantum speed-ups for solving Abelian hidden subgroup problems. We show that all…
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…
Faults are stochastic by nature while most man-made systems, and especially computers, work deterministically. This necessitates the linking of probability theory with mathematical logics, automata, and switching circuit theory. This paper…