Arithmetic on a Distributed-Memory Quantum Multicomputer

Distributed Quantum Computing (DQC) provides a means for scaling available quantum computation by interconnecting multiple quantum processor units (QPUs). A key challenge in this domain is efficiently allocating logical qubits from quantum circuits to the physical qubits within QPUs, a task known to be NP-hard. Traditional approaches, primarily focused on graph partitioning strategies, have sought to reduce the number of required Bell pairs for executing non-local CNOT operat...

Quantum physics is known to allow for completely new ways to create, manipulate and store information. Quantum communication - the ability to transmit quantum information - is a primitive necessary for any quantum internet. At its core, quantum communication generally requires the formation of entangled links between remote locations. The performance of these links is limited by the classical signaling time between such locations - necessitating the need for long lived quantu...

Near-term quantum computers can hold only a small number of qubits. One way to facilitate large-scale quantum computations is through a distributed network of quantum computers. In this work, we consider the problem of distributing quantum programs represented as quantum circuits across a quantum network of heterogeneous quantum computers, in a way that minimizes the overall communication cost required to execute the distributed circuit. We consider two ways of communicating:...

Richard Feynman's observation that quantum mechanical effects could not be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used quantum effects. This speculation appeared justified when Peter Shor described a polynomial time quantum algorithm for factoring integers. In quantum systems, the computational space increases exponentially with the size of the system which enables exponential parallelism. This...

In this paper we describe, implement, and test the performance of distributed memory simulations of quantum circuits on the MSU Laconia Top500 supercomputer. Using OpenMP and MPI hybrid parallelization, we first use a distributed matrix-vector multiplication with one-dimensional partitioning and discuss the shortcomings of this method due to the exponential memory requirements in simulating quantum computers. We then describe a more efficient method that stores only the $2^n$...

In recent years, interest in quantum computing has increased due to technological advances in quantum hardware and algorithms. Despite the promises of quantum advantage, the applicability of quantum devices has been limited to few qubits on hardware that experiences decoherence due to noise. One proposed method to get around this challenge is distributed quantum computing (DQC). Like classical distributed computing, DQC aims at increasing compute power by spreading the comput...

We propose a distributed quantum computing (DQC) architecture in which individual small-sized quantum computers are connected to a shared quantum gate processing unit (S-QGPU). The S-QGPU comprises a collection of hybrid two-qubit gate modules for remote gate operations. In contrast to conventional DQC systems, where each quantum computer is equipped with dedicated communication qubits, S-QGPU effectively pools the resources (e.g., the communication qubits) together for remot...

Quantum computers are able to outperform classical algorithms. This was long recognized by the visionary Richard Feynman who pointed out in the 1980s that quantum mechanical problems were better solved with quantum machines. It was only in 1994 that Peter Shor came up with an algorithm that is able to calculate the prime factors of a large number vastly more efficiently than known possible with a classical computer. This paradigmatic algorithm stimulated the flourishing resea...

The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route towards a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor's algorithm, weighted sum opt...

There are two central models considered in (fault-free synchronous) distributed computing: the CONGEST model, in which communication channels have limited bandwidth, and the LOCAL model, in which communication channels have unlimited bandwidth. Very recently, Le Gall and Magniez (PODC 2018) showed the superiority of quantum distributed computing over classical distributed computing in the CONGEST model. In this work we show the superiority of quantum distributed computing in ...