Related papers: Unitary Designs from Random Symmetric Quantum Circ…
Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the…
At its core a $t$-design is a method for sampling from a set of unitaries in a way which mimics sampling randomly from the Haar measure on the unitary group, with applications across quantum information processing and physics. We construct…
We investigate a class of brickwork-like quantum circuits on chains of $d-$level systems (qudits) that share the so-called `dual unitarity' property. Namely, these systems generate unitary dynamics not only when propagating in the time…
We provide two simple universality criteria. Our first criterion states that $\mathcal{S}\subset G_d:=U(d)$ is universal if and only if $\mathcal{S}$ forms a $\delta$-approximate $t(d)$-design, where $t(2)=6$ and $t(d)=4$ for $d\geq3$. Our…
A unitary state $t$-design is an ensemble of pure quantum states whose moments match up to the $t$-th order those of states uniformly sampled from a $d$-dimensional Hilbert space. Typically, unitary state $t$-designs are obtained by…
We use a random search technique to find quantum gate sequences that implement perfect quantum state preparation or unitary operator synthesis with arbitrary targets. This approach is based on the recent discovery that there is a large…
While quantum state tomography is notoriously hard, most states hold little interest to practically-minded tomographers. Given that states and unitaries appearing in Nature are of bounded gate complexity, it is natural to ask if efficient…
We present quantum circuits with a brick wall structure using the optimal number of parameters and two-qubit gates to parametrize $SU(2^n)$, and provide evidence that these circuits are universal for $n\leq 5$. For this, we successfully…
Say a collection of $n$-qu$d$it gates $\Gamma$ is eventually universal if and only if there exists $N_0 \geq n$ such that for all $N \geq N_0$, one can approximate any $N$-qu$d$it unitary to arbitrary precision by a circuit over $\Gamma$.…
This paper presents a deep reinforcement learning approach for synthesizing unitaries into quantum circuits. Unitary synthesis aims to identify a quantum circuit that represents a given unitary while minimizing circuit depth, total gate…
Kliuchnikov, Maslov, and Mosca proved in 2012 that a $2\times 2$ unitary matrix $V$ can be exactly represented by a single-qubit Clifford+$T$ circuit if and only if the entries of $V$ belong to the ring $\mathbb{Z}[1/\sqrt{2},i]$. Later…
The unitary design formation in random circuits has attracted considerable attention due to its wide range of practical applications and relevance to fundamental physics. While the formation rates in Haar random circuits have been…
Using geometric phases to realize noise-resilient quantum computing is an important method to enhance the control fidelity. In this work, we experimentally realize a universal nonadiabatic geometric quantum gate set in a superconducting…
TThe problem of finding the resource free, closest local unitary, to any bipartite unitary gate $U$ is addressed. Previously discussed as a measure of nonlocality, the distance $K_D(U)$ to the nearest product unitary has implications for…
A unitary 2-design can be viewed as a quantum analogue of a 2-universal hash function: it is indistinguishable from a truly random unitary by any procedure that queries it twice. We show that exact unitary 2-designs on n qubits can be…
We provide a systematic study on the possibility of supersymmetry (SUSY) for one dimensional quantum mechanical systems consisting of a pair of lines $\R$ or intervals [-l, l] each having a point singularity. We consider the most general…
For numerous applications of quantum theory it is desirable to be able to apply arbitrary unitary operations on a given quantum system. However, in particular situations only a subset of unitary operations is easily accessible. This raises…
How to find universal sets quantum gates (gates whose composition can form any othergate within a given range) is an important part of the development of quantum computation science that has been explored in the past with success. However,…
Quantum pseudorandomness, also known as unitary designs, comprise a powerful resource for quantum computation and quantum engineering. While it is known in theory that pseudorandom unitary operators can be constructed efficiently, realizing…
Unitary operations are the building blocks of quantum programs. Our task is to design effcient or optimal implementations of these unitary operations by employing the intrinsic physical resources of a given n-qubit system. The most common…