Related papers: Interactive shallow Clifford circuits: quantum adv…
There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A CNOT gate is however…
Quantum circuit compilation comprises many computationally hard reasoning tasks that nonetheless lie inside #$\mathbf{P}$ and its decision counterpart in $\mathbf{PP}$. The classical simulation of general quantum circuits is a core example.…
Recent discoveries in asymptotically good quantum codes have intensified research on their application in quantum computation and fault-tolerant operations. This study focuses on the addressability problem within CSS codes: what circuits…
State-of-the-art quantum computers can only reliably execute circuits with limited qubit numbers and computational depth. This severely reduces the scope of algorithms that can be run. While numerous techniques have been invented to exploit…
In a quantum computer, creating superpositions of quantum bits (qubits) in different states can lead to a speed-up over classical computers [1], but quantum mechanics also allows for the superposition of quantum circuits [2]. In fact, it…
Satisfiability Testing (SAT) techniques are well-established in classical computing where they are used to solve a broad variety of problems, e.g., in the design of classical circuits and systems. Analogous to the classical realm, quantum…
The Clifford group is a finite subgroup of the unitary group generated by the Hadamard, the CNOT, and the Phase gates. This group plays a prominent role in quantum error correction, randomized benchmarking protocols, and the study of…
$\text{MIP}^\ast$ is the class of languages decidable by an efficient classical verifier interacting with multiple quantum provers that share entangled qubits but cannot communicate. Notably, $\text{MIP}^\ast$ was proved to equal…
We study the classical simulatability of commuting quantum circuits with n input qubits and O(log n) output qubits, where a quantum circuit is classically simulatable if its output probability distribution can be sampled up to an…
In a recent work arXiv:2201.07655v2 we showed that there is a constant $\lambda >0$ such that it is possible to efficiently classically simulate a quantum system in which (i) qudits are placed on the nodes of a graph, (ii) each qudit…
In this paper we present the computational model underlying the one-way quantum computer which we introduced recently [Phys. Rev. Lett. 86, 5188 (2001)]. The one-way quantum computer has the property that any quantum logic network can be…
We describe a simple algorithm for sampling $n$-qubit Clifford operators uniformly at random. The algorithm outputs the Clifford operators in the form of quantum circuits with at most $5n + 2n^2$ elementary gates and a maximum depth of…
The intensive pursuit for quantum advantage in terms of computational complexity has further led to a modernized crucial question: {\it When and how will quantum computers outperform classical computers?} The next milestone is undoubtedly…
We introduce a low-overhead approach for detecting errors in arbitrary Clifford circuits on arbitrary qubit connectivities. Our method is based on the framework of spacetime codes, and is particularly suited to near-term hardware since it…
Modeling and simulation is essential for predicting and verifying the behavior of fabricated quantum circuits, but existing simulation methods are either impractically costly or require an unrealistic simplification of error processes. We…
Determining the quantum-classical boundary between quantum circuits which can be efficiently simulated classically and those which cannot remains a fundamental question. One approach to classical simulation is to represent the output of a…
We present evidence that there exist quantum computations that can be carried out in constant depth, using 2-qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically…
Classical simulations of quantum circuits are essential for verifying and benchmarking quantum algorithms, particularly for large circuits, where computational demands increase exponentially with the number of qubits. Among available…
While many statistical properties of deep random quantum circuits can be deduced, often rigorously and other times heuristically, by an approximation to global Haar-random unitaries, the statistics of constant-depth random quantum circuits…
The most general examples of quantum learning advantages involve data labeled by cryptographic or intrinsically quantum functions, where classical learners are limited by the infeasibility of evaluating the labeling functions using…