We compare different circuits implementing distributed versions of quantum computations, using entangled pairs only, and using distributed fan-out operations (using GHZ states). We highlight the advantages of using distributed fan-out operations in terms of reductions in circuit depth and (possibly) entanglement resources. We note that distributed fan-out operations (or notably, distributed GHZ states) could be a ``primitive'' building block for distributed quantum operations in the same way as entangled pairs are, if distributed GHZ states could be realized efficiently.
We compare different circuits implementing distributed versions of quantum computations, using entangled pairs only, and using distributed fan-out operations (using GHZ states). We highlight the advantages of using distributed fan-out operations in terms of reductions in circuit depth and (possibly) entanglement resources. We note that distributed fan-out operations (or notably, distributed GHZ states) could be a ``primitive'' building block for distributed quantum operations in the same way as entangled pairs are, if distributed GHZ states could be realized efficiently.
Much recent work on distributed quantum computing have focused on the use of entangled pairs and distributed two qubit gates. But there has also been work on efficient schemes for achieving multipartite entanglement between nodes in a single shot, removing the need to generate multipartite entangled states using many entangled pairs. This paper looks at how multipartite entanglement resources (e.g., GHZ states) can be useful for distributed fan-out operations; we also consider the use of qudits of dimension four for distributed quantum circuit compression. In particular, we consider how such fan-out operations and qudits can be used to implement circuits which are challenging for distributed quantum computation, involving pairwise qubit interactions, i.e., what has been called global gates (a.k.a. global Mølmer-Sørensen gates). Such gates have been explored to possibly yield more efficient computations via reduced circuit depth, and can be carried out efficiently in some types of quantum hardware (e.g., trapped-ion quantum computers); we consider this as an exploration of an ``extreme'' case for distribution given the global qubit-qubit interactions. We also conclude with some implications for future work on quantum circuit compilation and quantum data centre design.
A key problem in quantum computing is finding a viable technological path toward the creation of a scalable quantum computer. One possible approach toward solving part of this problem is distributed computing, which provides an effective way of utilizing a network of limited capacity quantum computers. In this paper, we present two primitive operations, cat-entangler and cat-disentangler, which in turn can be used to implement non-local operations, e.g. non-local CNOT and quantum teleportation. We also show how to establish an entangled pair, and use entangled pairs to efficiently create a generalized GHZ state. Furthermore, we present procedures which allow us to reuse channel qubits in a sequence of non-local operations. These non-local operations work on the principle that a cat-like state, created by cat-entangler, can be used to distribute a control qubit among multiple computers. Using this principle, we show how to efficiently implement non-local control operations in many situation, including a parallel implementation of a certain kind of unitary transformation. Finally, as an example, we present a distributed version of the quantum Fourier transform.
The main bottleneck for distributed quantum computing is the rate at which entanglement is produced between quantum processing units (QPUs). In this work, we prove that multiple QPUs connected through slow interconnects can outperform a monolithic architecture made with a single QPU. We consider a distributed quantum computing model with the following assumptions: (1) each QPU is linked to only two other QPUs, (2) each link produces only one Bell pair at a time, (3) the time to generate a Bell pair is τe times longer than the gate time. We propose a distributed version of the CliNR partial error correction scheme respecting these constraints and we show through circuit level simulations that, even if the entanglement generation time τe is up to five times longer than the gate time, distributed CliNR can achieve simultaneously a lower logical error rate and a shorter depth than both the direct implementation and the monolithic CliNR implementation of random Clifford circuits. In the asymptotic regime, we relax assumption (2) and we prove that links producing O(t/lnt) Bell pairs in parallel, where t is the number of QPUs, is sufficient to avoid stalling distributed CliNR, independently of the number of qubits per QPU. This demonstrates the potential of distributed CliNR for near-term multi-QPU devices. Moreover, we envision a distributed quantum superiority experiment based on the conjugated Clifford circuits of Bouland, Fitzsimons and Koh implemented with distributed CliNR.
Distributed quantum computing relies on coordinated operations between remote quantum processing units (QPUs), yet most existing work either assumes full connectivity, unrealistic for large networks, or relies on entanglement swapping. To mitigate the overhead of communication, we propose a scheme for the distribution of collective quantum operations among remote quantum processing units by exploiting distributed fan-out operations to a central node in network architectures similar to those used for high-performance computing, which requires only pre-shared entanglement, local operations and classical communication. We show that a general diagonal gate can be distributed among any number of nodes and provide the ebit cost bounds. For a single distributed multicontrolled gate, this amounts to a single additional Bell pair over the theoretically optimal calculation with all-to-all pre-shared entanglement, demonstrating better scalability when compared to current proposals based on entanglement swapping through a network. We provide a recipe for the lumped distribution of gates such as arbitrarily-sized Toffoli and multicontrolled Z, andRzz(θ)gates. Finally, we provide an exact implementation of a distributed Grover's search algorithm using this protocol to partition the circuit, with Bell pair cost growing linearly with the number of Grover iterations and the number of partitions, and show how these techniques can be applied to other algorithms such as QAOA. Our results show that alternative approaches to entanglement swapping can provide major benefits in distributed quantum computing, pointing to promising avenues for future research.
We present a distributed implementation of Shor's quantum factoring algorithm on a distributed quantum network model. This model provides a means for small capacity quantum computers to work together in such a way as to simulate a large capacity quantum computer. In this paper, entanglement is used as a resource for implementing non-local operations between two or more quantum computers. These non-local operations are used to implement a distributed factoring circuit with polynomially many gates. This distributed version of Shor's algorithm requires an additional overhead of O((log N)^2) communication complexity, where N denotes the integer to be factored.
Effective implementation of high-level quantum gates is essential for practical quantum computing. In this work, we presented, to the best of our knowledge, the first reported 12-CNOT decomposition of the double qubit excitation operator. We compared our new circuit with the previous SOTA 13-CNOT circuits in 4 different metrics. Our new circuit has the lowest CNOT count (12), lowest CNOT depth (8, roughly 27% reduction), and lowest total circuit depth (15, 25% reduction) among all the previous SOTA circuits. With output qubit relabeling, the CNOT depth can be further reduced to 7 (roughly 36% reduction from 11). Further, we only added 2 extra 1q gates (from 11 to 13) compared to the best of the SOTA circuits. As the double qubit excitation operator can be used as a building block hundreds or thousands of times in practical quantum algorithms, any reduction in such primitives compounds over the full circuit, resulting in significant overall resource savings.