Related papers: Computation at a distance
We are considering RAMs $N_{n}$, with wordlength $n=2^{d}$, whose arithmetic instructions are the arithmetic operations multiplication and addition modulo $2^{n}$, the unary function $ \min\lbrace 2^{x}, 2^{n}-1\rbrace$, the binary…
We consider the communication capacity of wireline networks for a two-unicast traffic pattern. The network has two sources and two destinations with each source communicating a message to its own destination, subject to the capacity…
Prior work has shown that there exists a relation problem which can be solved with certainty by a constant-depth quantum circuit composed of geometrically local gates in two dimensions, but cannot be solved with high probability by any…
We investigate the theoretical limits of the effect of the quantum interaction distance on the speed of exact quantum addition circuits. For this study, we exploit graph embedding for quantum circuit analysis. We study a logical mapping of…
Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and…
A function computation problem in directed acyclic networks has been considered in the literature, where a sink node wants to compute a target function with the inputs generated at multiple source nodes. The network links are error-free but…
We identify a common scheme in several existing algorithms addressing computational problems on linear differential equations with polynomial coefficients. These algorithms reduce to computing a linear relation between vectors obtained as…
We present a novel automated technique for parallelizing quantum circuits via forward and backward translation to measurement-based quantum computing patterns and analyze the trade off in terms of depth and space complexity. As a result we…
We show that the quantum parity gate on $n > 3$ qubits cannot be cleanly simulated by a quantum circuit with two layers of arbitrary C-SIGN gates of any arity and arbitrary 1-qubit unitary gates, regardless of the number of allowed ancilla…
Noisy, intermediate-scale quantum computers come with intrinsic limitations in terms of the number of qubits (circuit "width") and decoherence time (circuit "depth") they can have. Here, for the first time, we demonstrate a recently…
The increasing depth of quantum circuits presents a major limitation for the execution of quantum algorithms, as the limited coherence time of physical qubits leads to noise that manifests as errors during computation. In this work, we…
Of the many potential hardware platforms, superconducting quantum circuits have become the leading contender for constructing a scalable quantum computing system. All current architecture designs necessitate a 2D arrangement of…
We study space-bounded communication complexity for unitary implementation in distributed quantum processors, where we restrict the number of qubits per processor to ensure practical relevance and technical non-triviality. We model…
We study a reduced quantum circuit computation paradigm in which the only allowable gates either permute the computational basis states or else apply a "global Hadamard operation", i.e. apply a Hadamard operation to every qubit…
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
Motivated by the recent experimental demonstrations of quantum supremacy, proving the hardness of the output of random quantum circuits is an imperative near term goal. We prove under the complexity theoretical assumption of the…
Classical simulations of quantum circuits are limited in both space and time when the qubit count is above 50, the realm where quantum supremacy reigns. However, recently, for the low depth circuit with more than 50 qubits, there are…
Present quantum computers are constrained by limited qubit capacity and restricted physical connectivity, leading to challenges in large-scale quantum computations. Distributing quantum computations across a network of quantum computers is…
Simulations of quantum dynamics are a key application of near term quantum computing, but are hindered by the twin challenges of noise and small device scale, which limit the executable circuit depths and the number of qubits the algorithm…