Related papers: A simpler proof of zero-knowledge against quantum …
We examine how amplitude noise in queries to the oracle degrades a performance of quantum search algorithm. The Grover search and similar techniques are widely used in various quantum algorithms, including cases where rival parties are…
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably…
This paper proves that classical-witness quantum Merlin-Arthur proof systems can achieve perfect completeness. That is, QCMA = QCMA1. This holds under any gate set with which the Hadamard and arbitrary classical reversible transformations…
We show how phase and amplitude estimation algorithms can be parallelized. This can reduce the gate depth of the quantum circuits to that of a single Grover operator with a small overhead. Further, we show that for quantum amplitude…
We construct reversible Boolean circuits efficiently simulating reversible Turing machines. Both the circuits and the simulation proof are rather simple. Then we give a fairly straightforward generalization of the circuits and the…
Functional validation is necessary to detect any errors during quantum computation. There are promising avenues to debug quantum circuits using runtime assertions. However, the existing approaches rely on the expertise of the verification…
Grover's algorithm, orginally conceived as a means of searching an unordered database, can also be used to extract solutions from the result sets generated by quantum computations. The Grover algorithm exploits the concept of an oracle…
A proof of quantumness is an efficiently verifiable interactive test that an efficient quantum computer can pass, but all efficient classical computers cannot (under some cryptographic assumption). Such protocols play a crucial role in the…
This paper presents stronger methods of achieving perfect completeness in quantum interactive proofs. First, it is proved that any problem in QMA has a two-message quantum interactive proof system of perfect completeness with constant…
We describe a simulation method for a quantum spin model of a generic, general purpose quantum computer. The use of this quantum computer simulator is illustrated through several implementations of Grover's database search algorithm. Some…
Grover's algorithm, a well-know quantum search algorithm, allows one to find the correct item in a database, with quadratic speedup. In this paper we adapt Grover's algorithm to the problem of finding a correct answer to a natural language…
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…
We describe a simple quantum algorithm for preparing $K$ copies of an $N$-dimensional quantum state whose amplitudes are given by a quantum oracle. Our result extends a previous work of Grover, who showed how to prepare one copy in time…
A brief review is given of the physical implementation of quantum computation within spin systems or other two-state quantum systems. The importance of the controlled-NOT or quantum XOR gate as the fundamental primitive operation of quantum…
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.…
Quantum Amplitude Amplification (QAA), the generalization of Grover's algorithm, is capable of yielding optimal solutions to combinatorial optimization problems with high probabilities. In this work we extend the conventional 2-dimensional…
Unstructured search remains as one of the significant challenges in computer science, as classical search algorithms become increasingly impractical for large-scale systems due to their linear time complexity. Quantum algorithms, notably…
In this paper, we show that the zero-knowledge construction for Hamiltonian cycle remains secure against quantum adversaries in the relativistic setting. Our main technical contribution is a tool for studying the action of consecutive…
The phase conjugation of an unknown Gaussian state cannot be realized perfectly by any physical process. A semi-classical argument is used to derive a tight lower bound on the noise that must be introduced by an approximate phase…
Quantum algorithms use the principles of quantum mechanics, as for example quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimisation,…