Related papers: Space-Efficient and Noise-Robust Quantum Factoring
Scalable quantum computing is based on realizable accurate quantum gates. For neutral atoms, it is an outstanding challenge to design a high-fidelity two-qubit entangling gate without resorting to difficult techniques like shaping laser…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
We study the encoding complexity for quantum error correcting codes with large rate and distance. We prove that random Clifford circuits with $O(n \log^2 n)$ gates can be used to encode $k$ qubits in $n$ qubits with a distance $d$ provided…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
A common starting point of traditional quantum algorithm design is the notion of a universal quantum computer with a scalable number of qubits. This convenient abstraction mirrors classical computations manipulating finite sets of symbols,…
Shor's quantum factoring algorithm finds the prime factors of a large number exponentially faster than any other known method a task that lies at the heart of modern information security, particularly on the internet. This algorithm…
With the advancement of quantum technologies, there is a potential threat to traditional encryption systems based on integer factorization. Therefore, developing techniques for accurately measuring the performance of associated quantum…
In near-term quantum computations that do not employ error correction, noise can proliferate rapidly, corrupting the quantum state and making results unreliable. These errors originate from both decoherence and control imprecision. The…
Optimizing quantum circuits is critical: the number of quantum operations needs to be minimized for a successful evaluation of a circuit on a quantum processor. In this paper we unify two disparate ideas for optimizing quantum circuits,…
Advancements in quantum computing have spurred significant interest in harnessing its potential for speedups over classical systems. However, noise remains a major obstacle to achieving reliable quantum algorithms. In this work, we present…
Nonlinear boolean equation systems play an important role in a wide range of applications. Grover's algorithm is one of the best-known quantum search algorithms in solving the nonlinear boolean equation system on quantum computers. In this…
We discuss the realization of a universal set of ultrafast single- and two-qubit operations with superconducting quantum circuits and investigate the most relevant physical and technical limitations that arise when pushing for faster and…
We propose a method for quantum noise extraction from the interference of laser pulses with random phase. Our technique is based on the calculation of a parameter, which we called the quantum reduction factor, and which allows determining…
We show that given the order of a single element selected uniformly at random from $\mathbb Z_N^*$, we can with very high probability, and for any integer $N$, efficiently find the complete factorization of $N$ in polynomial time. This…
Recent quantum technologies and quantum error-correcting codes emphasize the requirement for arranging interacting qubits in a nearest-neighbor (NN) configuration while mapping a quantum circuit onto a given hardware device, in order to…
Quantum computing is a rapidly expanding field with applications ranging from optimization all the way to complex machine learning tasks. Quantum memories, while lacking in practical quantum computers, have the potential to bring quantum…
Distributed quantum computation is the key to high volume computation in the NISQ era. This investigation explores the key aspects necessary for the construction of a quantum network by numerically simulating the execution of the…
Quantum Variational Circuits (QVCs) are often claimed as one of the most potent uses of both near term and long term quantum hardware. The standard approaches to optimizing these circuits rely on a classical system to compute the new…
Quantum algorithm design usually assumes access to a perfect quantum computer with ideal properties like full connectivity, noise-freedom and arbitrarily long coherence time. In Noisy Intermediate-Scale Quantum (NISQ) devices, however, the…
Quantum computers are capable of efficiently contracting unitary tensor networks, a task that is likely to remain difficult for classical computers. For instance, networks based on matrix product states or the multi-scale entanglement…