Linked Quantum Computers Overcome Noise to Boost Processing Power

Researchers are increasingly focused on distributed quantum computing as a viable route towards scaling quantum computation to tackle complex problems. Leo Sünkel, Michael Kölle, and Tobias Rohe, from the Institute for Informatics LMU Munich, alongside Claudia Linnhoff-Popien et al., present a detailed evaluation of the Remote CX protocol, a key technique for applying quantum gates between spatially separated qubits, under realistic noisy conditions. This work significantly advances the field by providing a high-level framework to assess protocol performance across diverse network configurations and qubit assignment strategies, utilising Grover, GHZ, VQC, and random circuits. The findings illuminate how both quantum processing unit (QPU) architecture and scheduling choices can detrimentally affect fidelity, offering crucial insights for optimising future distributed quantum systems.

Remote CX gate fidelity under network noise and qubit assignment strategies are critical for scalable quantum computation

Scientists are increasingly exploring distributed quantum computing as a potential pathway to scaling quantum computing to capacities necessary for practical and large-scale applications. Connecting multiple quantum processing units (QPUs) in clusters or over networks requires entanglement to be generated and distributed over distances.
Using entanglement, the remote CX protocol can be performed, allowing the application of the CX gate involving qubits located in different QPUs. The results provide insights on how QPU and network configurations or naive scheduling can degrade performance. Distributed quantum computing is an emerging paradigm in which circuits are executed on multiple connected quantum processing units (QPUs).

Enabling distributed quantum computing on large networks poses significant challenges, especially for networks akin to a quantum Internet. Entanglement is a central component of such networks and is required for quantum communication. Unfortunately, qubits are fragile, and establishing and maintaining entanglement over distance for a prolonged time is a major challenge that requires specialized hardware with the ability to run certain communication protocols.

Quantum repeaters, performing entanglement swapping and purification protocols, can be placed throughout the network, thereby enabling quantum communication over larger distances. Entanglement swapping allows the establishment of entanglement between nodes without requiring them to interact directly with each other, while the purification protocol can increase entanglement fidelity.

Providing the hardware to enable distributing and maintaining highly entangled qubits is not the only challenge; novel algorithms and software tools are also being heavily investigated by the research community. For instance, qubits must be assigned to nodes in the network and circuits compiled accordingly.

Furthermore, algorithms and applications are also being evaluated, including chemistry, variational quantum algorithms, and a distributed version of Shor’s algorithm. Performing remote operations between QPUs requires entanglement, which must be established and distributed in the network, and is ultimately consumed in the process.

Thus, entanglement is often considered a key resource that should not be used wastefully. Naive qubit assignment and circuit partitioning may result in unnecessary remote operations, exhausting limited resources which could otherwise be avoided. The network configuration, i.e., what type of QPUs and how they are connected, or the circuit architecture may also be a contributing factor and influence the performance.

The aim of this work is to evaluate how distributed versions of circuits perform under noise in comparison to their original monolithic counterparts. The distributed versions of the circuits are constructed for different network architectures, that is, different numbers of QPUs as well as qubit capacities.

However, the simulations use a simplified model; more specifically, researchers do not use a full network simulator that applies networking protocols such as entanglement swapping or purification, nor does the model contain repeaters or entanglement generation over distance. Instead, the focus lies on a high-level evaluation of how remote operations, i.e., remote CX gates, which are added as a protocol to the circuit, influence the overall performance of the circuit measured in fidelity.

In quantum networking, QPUs can reserve qubits for computation and communication, where the former can be seen as the logical qubits in a monolithic circuit and the latter are only used for communicating between QPUs. Different configurations (e.g., more communication qubits allow for more remote operations to be applied in parallel) result in a different distributed circuit, and thus required remote operations and resources.

To this end, the investigation focuses on how different QPU configurations have an impact on the overall computation. In an experimental evaluation, distributed circuits are constructed according to their QPU configuration and simulated under noise. Additionally, the qubit schedule, that is, the assignment of qubits to QPUs, affects the performance.

Researchers begin with a short overview of the essentials of quantum computing and continue with quantum networks. In quantum computing, the most fundamental unit of information is encoded in a qubit, a two-state system similar to a bit in classical computing. However, unlike a classical bit, a qubit can be in a superposition of states, whereas a classical bit is either in state 0 or 1 at any given time.

The state of a qubit can be defined as |ψ⟩= α |0⟩+ β |1⟩ with α and β being complex numbers representing probability amplitudes where |α|2 and |β|2 give the probabilities of the qubit being in state 0 or 1 after measurement where |α|2 + |β|2 = 1. A qubit is in a quantum state until it’s measured; after measurement the qubit collapses to the corresponding basis state.

Entanglement is a further important property. When qubits are entangled, their measurement outcomes correlate, allowing one to infer information about the others, even if the qubits are far apart. Bell states are maximally entangled two qubit states and are defined as Φ+ = 1/√2(|00⟩+|11⟩), Φ−= 1/√2(|00⟩−|11⟩), Ψ+ = 1/√2(|01⟩+|10⟩), and Ψ−= 1/√2(|01⟩−|10⟩).

A quantum network can be defined as a graph G = (N, E) with nodes N and edges E where N are quantum devices (e.g., QPUs or repeaters) and E communication channels. Both quantum and classical channels are required for certain protocols. The crucial requirement for quantum communication is entanglement, which must be created and distributed throughout the network.

However, to establish and maintain entanglement over large distances, quantum repeaters performing entanglement purification and swapping are required. By applying a purification protocol on n weakly entangled qubits, m highly entangled qubits can be established, where m The protocol involves two Bell pairs and three parties.

A Bell measurement can now be performed on the qubits located at C, thereby projecting the entanglement onto A and B, establishing an entangled link between them without requiring direct communication between the nodes. A qubit’s state can be teleported to different nodes in the network, requiring a Bell pair established between two QPUs and allowing one to transfer a qubit’s state to another.

The state, however, is destroyed at its original location. In distributed quantum computing, a quantum circuit is run on multiple connected QPUs simultaneously. Qubits are assigned to QPUs and the circuit is divided into subcircuits which are then distributed to the nodes.

When a CX gate where the involved qubits are located in different QPUs must be executed, a remote operation must be performed. One possible solution is to transfer the state of a qubit through the teleportation protocol such that all necessary qubits are located in the same QPU, allowing the gate to be executed locally.

Another option is to use the remote CX protocol. Both protocols require entanglement in the form of a Bell pair. Which protocol to use depends on the context.

Previous authors have presented simulation frameworks and evaluated different quantum algorithms in the DQC setting, including the variational quantum eigensolver and quantum k-means clustering. Another DQC simulation framework is presented in, where the authors also evaluate their approach with various algorithms.

A performance analysis of DQC is given in, variational quantum eigensolvers for DQC are discussed in, and the architecture of variational quantum circuits in the context of DQC was evaluated in. The simulation framework used in this work is based on the approach presented in that paper. DQC for chemical applications are discussed in.

In the first part of this section, the approach used to construct and simulate the distributed circuits is introduced. In the second part, an overview of the experimental setup is given. The number of available QPUs and their respective capabilities influence the required number of remote operations, which in turn can affect the performance.

Distributed quantum circuit execution and qubit assignment strategies are crucial for scalability

A specialized framework was employed for high-level evaluation of remote CX gate protocol performance under noise in various network configurations. All circuits were transpiled using X, RZ, H, and CX basis gates to prepare them for distributed execution. Two distinct qubit assignment methods were implemented and compared.

A naive approach sequentially filled each quantum processing unit (QPU), assigning the first two qubits to QPU 0, the next two to QPU 1, and so on. Alternatively, a graph partitioning (GP) technique converted circuits into graphs representing qubits as nodes and CX gates as weighted edges, excluding single-qubit gates.

PyMetis was used to perform the graph partitioning, optimizing qubit allocation across QPUs. The performance of monolithic circuits was contrasted with distributed versions utilizing two, four, and eight QPUs, each with varying numbers of computational and communication qubits as detailed in Table I. For the Grover circuit, a monolithic configuration achieved a fidelity of 0.87 under noise, while a distributed version with two QPUs attained a fidelity of 0.70.

Experiments with the GHZ circuit showed a monolithic fidelity of 0.97, decreasing to 0.95, 0.92, and 0.85 with two, four, and eight QPUs respectively, with both schedules yielding identical mean performance. Analysis of the VQC circuit with eight qubits revealed a monolithic fidelity of 0.87, and distributed fidelities of 0.76, 0.66, and 0.51 for two, four, and eight QPUs.

Circuit depth was also measured to assess the efficiency of each scheduling method. For the VQC circuit with eight qubits, the depth remained consistent between naive and optimized schedules. However, for random circuits, the optimized schedule demonstrated shallower circuits in the two and four QPU cases, indicating improved performance through strategic qubit assignment. Results from the eight and twelve qubit random circuits further highlighted the benefits of the optimized schedule, particularly with fewer QPUs, where significant fidelity improvements were observed.

Fidelity assessment of distributed quantum circuits utilising remote two-qubit gates is crucial for scalable quantum computation

Scientists evaluated the performance of circuits distributed across multiple quantum processing units (QPUs) under noisy conditions. The study focused on high-level evaluation of remote operations and their influence on overall circuit performance, measured in fidelity, rather than implementing a full network simulator.

Different QPU configurations, varying in the number of QPUs and qubit capacities, were constructed to create distributed circuits. Simulations revealed how these configurations impact the overall computation, with the framework reserving qubits for both computation and communication. Evaluations included assessments of qubit scheduling, specifically the assignment of qubits to QPUs, and its effect on performance.

The work did not incorporate networking protocols like entanglement swapping or purification, or models containing repeaters or entanglement generation over distance, concentrating instead on the fidelity impact of added remote CX gates. The research explored how naive and graph partitioning qubit assignment strategies influence fidelity.

Qubit assignment and circuit partitioning were investigated to determine if unnecessary remote operations exhaust limited resources. Network configuration and circuit architecture were also considered as potential factors influencing performance. Distributed circuits were constructed for various network architectures, allowing for analysis of how different configurations affect the required remote operations and resources.

A qubit’s state can be defined as |ψ⟩= α |0⟩+ β |1⟩, where α and β are complex numbers representing probability amplitudes, and |α|2 + |β|2 equals 1. Entangled qubits exhibit correlated measurement outcomes, even when separated by distance, and Bell states, such as Φ+ = 1/√2(|00⟩+|11⟩), serve as maximally entangled two-qubit states. These states, often referred to as Bell or EPR pairs, are fundamental to quantum networking.

Entanglement fidelity is contingent on processor allocation and network scale, impacting overall quantum communication performance

Distributed quantum computing offers a potential route to scaling computational capacity beyond the limitations of individual quantum processing units. This approach involves connecting multiple processors via classical and quantum channels, enabling the execution of circuits too large for any single device.

Central to this paradigm is the remote controlled-X gate protocol, which facilitates operations between qubits located on different processors, requiring the generation and distribution of entanglement. Recent investigations have evaluated the performance of distributed circuits employing this protocol under noisy conditions, assessing various network configurations and qubit assignment strategies.

Results indicate that increasing the number of processors generally reduces circuit fidelity, with performance significantly impacted by how qubits are assigned to each processor. However, for circuits exhibiting specific entanglement patterns, where controlled-X gates primarily connect neighbouring qubits, naive assignment strategies can yield comparable results to optimized scheduling.

The simulations employed a simplified noise model and communication framework to investigate performance across different scenarios and configurations. The findings highlight the importance of resource management, particularly entanglement, in distributed quantum computing. Establishing and maintaining entanglement between distant nodes is resource intensive, necessitating optimized scheduling to minimise unnecessary consumption.

While the current study utilized a simplified model, it provides valuable initial insights into the challenges of scaling distributed quantum computation. Future research should focus on incorporating more realistic network topologies, entanglement generation techniques, and exploring the relationship between circuit architecture and optimal qubit assignment to processors, ultimately aiming to maintain high fidelity in larger, more complex distributed quantum systems.