Related papers: Classical analog circuit emulation of quantum Grov…
These notes begin in Chapter 1 with a review of linear algebra and the postulates of quantum mechanics, leading to an explanation of single- and multi-qubit gates. Chapter 2 explores the challenge of constructing arbitrary quantum states…
Quantum information science strives to leverage the quantum-mechanical nature of our universe in order to achieve large improvements in certain information processing tasks. In deep-space optical communications, current receivers for the…
Quantum Computing offers an entirely new way of doing computation governed by the rules of quantum mechanics like Superposition and Entanglement. These rules allow us to do computation over all the possible states simultaneously. Hence,…
The quantum Fourier transform (QFT) is sometimes said to be the source of various exponential quantum speed-ups. In this paper we introduce a class of quantum circuits which cannot outperform classical computers even though the QFT…
In Ref. [Phys. Rev. A 100, 062317 (2019)], the authors reported an algorithm to implement, in a circuit-based quantum computer, a general quantum measurement (GQM) of a two-level quantum system, a qubit. Even though their algorithm seems…
Quantum circuit simulations are critical for evaluating quantum algorithms and machines. However, the number of state amplitudes required for full simulation increases exponentially with the number of qubits. In this study, we leverage data…
The ability to perform quantum error correction (QEC) and robust gate operations on encoded qubits opens the door to demonstrations of quantum algorithms. Contemporary QEC schemes typically require mid-circuit measurements with feed-forward…
It is shown that irreversible classical cellular automata can be performed by quantum algorithm using additional ancilla registers. The algorithm for cellular automata states analysis has been proposed. This algorithm is based on the…
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 define a formal framework for equivalence checking of sequential quantum circuits. The model we adopt is a quantum state machine, which is a natural quantum generalisation of Mealy machines. A major difficulty in checking quantum…
As the engineering endeavour to realise quantum computers progresses, we consider that such machines need not rely on binary as their de facto unit of information. We investigate Grover's algorithm under a generalised quantum circuit model,…
We study operator scrambling in quantum circuits built from `super-Clifford' gates. For such circuits it was established in arXiv:2002.12824 that the time evolution of operator entanglement for a large class of many-body operators can be…
In this work I describe a classical analog of Grover's quantum searching algorithm, explaining why a quantum algorithm should be able to perform search in O(sqrtN) steps and also acting as a useful pedagogic demonstration.
In this paper we present a simulation environment enhanced with parallel processing which can be used on personal computers, based on a high-level user interface developed on Mathematica\copyright which is connected to C++ code in order to…
In recent times, Variational Quantum Circuits (VQC) have been widely adopted to different tasks in machine learning such as Combinatorial Optimization and Supervised Learning. With the growing interest, it is pertinent to study the…
We apply quantum homomorphic encryption (QHE) schemes suitable for circuits with a polynomial number of $T/T^{\dagger}$-gates to Grover's algorithm, performing a simulation in Qiskit of a Grover circuit that contains 3 qubits. The…
Grover's search algorithm was originally proposed for circuit-based quantum computers. A crucial part of it is to query an oracle -- a black-box unitary operation. Generation of this oracle is formally beyond the original algorithm design.…
Grover's search algorithm is one of the first quantum algorithms to exhibit a provable quantum advantage. It forms the backbone of numerous quantum applications and is widely used in benchmarking efforts. Here, we report…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
The number of measurements necessary to perform the quantum state reconstruction of a system of qubits grows exponentially with the number of constituents, creating a major obstacle for the design of scalable tomographic schemes. We work…