Related papers: Quantum circuits and low-degree polynomials over F…
We introduce a new scheme for quantum circuit design called controlled gate networks. Rather than trying to reduce the complexity of individual unitary operations, the new strategy is to toggle between all of the unitary operations needed…
Many quantum algorithms can be represented in a form of a classical circuit positioned between quantum Fourier transformations. Motivated by the search for new quantum algorithms, we turn to circuits where the latter transformation is…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
This paper describes an ACL2 interpreter for "netlists" describing quantum circuits. Several quantum gates are implemented, including the Hadamard gate H, which rotates vectors by 45 degrees, necessitating the use of irrational numbers, at…
Can near-term gate model based quantum processors offer quantum advantage for practical applications in the pre-fault tolerance noise regime? A class of algorithms which have shown some promise in this regard are the so-called…
This is an exposition of some basic mathematical aspects of quantum logic gates. At first we established some general formulas for the case of arbitrary quantum gate A with unique restriction A^2=I. The explicit form of the generators and…
In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower…
Universal quantum computation may be realized based on quantum walk, by formulating it as a scattering problem on a graph. In this paper, we simulate quantum gates through electric circuits, following a recent report that a one-dimensional…
Digital-analog quantum computing with two-level systems is a computational paradigm that combines an analog Hamiltonian with single-qubit gates to achieve universality. We extend this framework to $d$-level systems by conjugating an analog…
Recent work of Bravyi et al. and follow-up work by Bene Watts et al. demonstrates a quantum advantage for shallow circuits: constant-depth quantum circuits can perform a task which constant-depth classical (i.e., AC$^0$) circuits cannot.…
This tutorial guides a competent programmer through the crafting of a quantum circuit simulator from scratch, even for readers with almost no prior experience in quantum computing. Open source simulators for quantum circuits already exist,…
We show a relation, based on parallel repetition of the Magic Square game, that can be solved, with probability exponentially close to $1$ (worst-case input), by $1D$ (uniform) depth $2$, geometrically-local, noisy (noise below a…
In breakthrough work, Bravyi, Gosset, and K\"{o}nig (BGK) [Science, 2018] unconditionally proved that constant depth quantum circuits are more powerful than their classical counterparts. Their result is equivalent to saying that a…
The implementation of holonomic quantum computation on superconducting quantum circuits is challenging due to the general requirement of controllable complicated coupling between multilevel systems. Here we solve this problem by proposing a…
Although many of works have been done in multivalued quantum logic synthesis, the question whether multivalued quantum circuits are more efficient than the conventional binary quantum circuits is still open. In this article we devote to the…
Quantum circuit simulation is paramount to the verification and optimization of quantum algorithms, and considerable research efforts have been made towards efficient simulators. While circuits often contain high-level gates such as oracles…
We propose an implementation of a two-dimensional $\mathbb{Z}_2$ lattice gauge theory model on a shallow quantum circuit, involving a number of single and two-qubits gates comparable to what can be achieved with present-day and near-future…
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…
Quantum computers can efficiently solve problems which are widely believed to lie beyond the reach of classical computers. In the near-term, hybrid quantum-classical algorithms, which efficiently embed quantum hardware in classical…
In recent years simulations of chemistry and condensed materials has emerged as one of the preeminent applications of quantum computing, offering an exponential speedup for the solution of the electronic structure for certain strongly…