Related papers: Classical simulability of quantum circuits followe…
The complexity of simulating quantum many-body dynamics, or quantum computations, in the Heisenberg picture is governed by the scrambling of initially simple operators into superpositions of exponentially many Pauli strings. The…
Using the tensor product representation in the density matrix renormalization group, we show that a quantum circuit of Grover's algorithm, which has one-qubit unitary gates, generalized Toffoli gates, and projective measurements, can be…
Permutational Quantum Computing (PQC) [\emph{Quantum~Info.~Comput.}, \textbf{10}, 470--497, (2010)] is a natural quantum computational model conjectured to capture non-classical aspects of quantum computation. An argument backing this…
We prove that any perfect quantum strategy for the two-prover game encoding a constraint satisfaction problem (CSP) can be simulated via a perfect classical strategy with an extra classical communication channel, whose size depends only on…
Understanding which subclasses of quantum circuits are efficiently classically simulable is fundamental to delineating the boundary between classical and quantum computation. In this context, it is well known that certain tasks based on…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
Simulations of collisions of fundamental particles on a quantum computer are expected to have an exponential advantage over classical methods and promise to enhance searches for new physics. Furthermore, scattering in scalar field theory…
The Gottesman-Knill theorem asserts that quantum circuits composed solely of Clifford gates can be efficiently simulated classically. This theorem hinges on the fact that Clifford gates map Pauli strings to other Pauli strings, thereby…
Recent demonstrations of superconducting quantum computers by Google and IBM and trapped-ion computers from IonQ fueled new research in quantum algorithms, compilation into quantum circuits, and empirical algorithmics. While online access…
In recent times, Variational Quantum Circuits (VQC) have been widely adopted to different tasks in machine learning such as Combinatorial Optimization and Supervised Learning. With the growing interest, it is pertinent to study the…
Quantum Supremacy is a demonstration of a computation by a quantum computer that can not be performed by the best classical computer in a reasonable time. A well-studied approach to demonstrating this on near-term quantum computers is to…
Quantum processing unit (QPU) has to satisfy highly demanding quantity and quality requirements on its qubits to produce accurate results for problems at useful scales. Furthermore, classical simulations of quantum circuits generally do not…
In this study, a distinctive feature of quantum computation (QC) is characterized. To this end, a seemingly-powerful classical computing model, called "stochastic ensemble machine (SEnM)," is considered. The SEnM runs with an ensemble…
Classical simulation of quantum computation has often been viewed as the method to determine where the horizon of quantum supremacy is located---that is, where quantum computation can no longer be simulated by classical methods. As of now,…
A quantum state is called concordant if it has zero quantum discord with respect to any part. By extension, a concordant computation is one such that the state of the computer, at each time step, is concordant. In this paper, I describe a…
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…
We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
The rapid scaling of superconducting quantum computers has highlighted the impact of device-level variability on overall circuit fidelity. In particular, fabrication-induced fluctuations in device parameters such as capacitance and…
We discuss a new approach to simulate quantum algorithms using classical probabilistic bits and circuits. Each qubit (a two-level quantum system) is initially mapped to a vector in an eight dimensional probability space (equivalently, to a…