NVIDIA CUDA-Q Runs Breakthrough Logical Qubit Application on Infleqtion QPU

Infleqtion, a world leader in neutral atom quantum computing, used the NVIDIA CUDA-Q platform to first simulate, and then orchestrate the first-ever demonstration of a material science experiment on logical qubits, on their Sqale physical quantum processing unit (QPU). 

Qubits, the basic units of information in quantum computing, are prone to errors, and far too unreliable to make meaningful predictions. Logical qubits, collections of many noisy physical qubits that encode quantum information such that errors can be corrected, overcome this limitation. Logical qubits can perform quantum computations that are tolerant to environmental noise and hardware faults, also known as fault tolerant quantum computing.

A key test for logical qubits is observing a reduced error rate compared to their constituent, noisy, physical qubits. Infleqtion’s results demonstrate this convincingly across a spectrum of inputs (Figure 1).

This is a major first step towards fault-tolerant quantum computing, and one of only a few physical demonstrations of an application using logical qubits. 

This post explores the CUDA-Q features and performance that were essential to this breakthrough work. It also outlines how you can use CUDA-Q to build your own end-to-end logical qubit workflow on Infleqtion hardware.

Logical qubits for materials science 

The discovery and development of novel materials is often accelerated by simulation. Accurate simulation can help predict new candidate materials by reducing the necessity of performing expensive and slow experiments. 

Strongly correlated materials, often some of the most interesting, are notoriously difficult to simulate because of the complex ways in which their electrons interact. Such systems cause many approximate methods to break down and require simulation with exponentially costly methods to properly capture their physics.

One such method is dynamical mean-field theory (DMFT), which can accurately describe strongly correlated systems, but at the cost of exponential scaling. This has motivated researchers to explore using quantum computers to perform accurate DMFT simulations at much larger scales.

Infleqtion’s work demonstrates a fault-tolerant preparation of the ground state of the single-impurity Anderson model using two logical qubits, a key step towards fault-tolerant DMFT.  

Each logical qubit is encoded with a [[4,2,2]] error detection code (Figure 2). This encodes two logical qubits as four physical qubits where a single X-type error (bit flip) or a single Z-type error (phase flip) can be detected and discarded but not corrected. Errors are detected by measuring the encoded states and determining the parity (number of 1s) in the result, with an odd parity indicating an error.  

This error detection process allows failed circuit runs (where an error was detected) to be discarded. In cases where the physical qubit error rate is above a certain threshold (determined by experiment) this has the net effect of improving the overall quality of results.

Creating an end-to-end workflow with CUDA-Q integration

A pivotal factor in the success of these experiments was the seamless integration of CUDA-Q with Infleqtion’s gate-based neutral atom quantum computer, creating a comprehensive end-to-end workflow. With CUDA-Q and its industry-leading simulators, Infleqtion developed and tested their code efficiently, then trivially transitioned to executing the same code on their neutral atom QPU.

In designing and modeling their experiment, Infleqtion used CUDA-Q to leverage GPU-accelerated simulations, including the emulation of parallel computation across multiple QPUs. The CUDA-Q parameterized kernel simplified this task, along with the new CUDA-Q Solvers library of common algorithm primitives. Defining custom gate operations using CUDA-Q also enabled Infleqtion to implement custom gates native to their hardware and use them in conjunction with custom circuit noise models to emulate the unique noise profile of their neutral atom QPU.

These customized simulations, together with CUDA-Q mid-circuit measurement and conditional logic capabilities meant that the performance of the [[4,2,2]] code could be fully simulated. Having determined the most effective way to run the experiment, Infleqtion simply changed the target in their CUDA-Q code to run directly on their neutral atom QPU.  

Running CUDA-Q applications on Infleqtion hardware

By obtaining Infleqtion API key permissions, users can now reproduce their work in modeling and running logical qubit experiments. Under the hood, Infleqtion’s cross-platform Superstaq compiler performs low-level compilation to the device physics and gateset. This enables users to easily run CUDA-Q applications on Infleqtion hardware by simply specifying one of the following targets.

# Example Bell Circuit
@cudaq.kernel
def kernel():
    qubits = cudaq.qvector(2)
    h(qubits)
    cx(qubits[0], qubits[1])
    mz(qubits)

# Enter Infleqtion API key
export SUPERSTAQ_API_KEY=”<insert key>”

# Run on Infleqtion QPU
cudaq.set_target("infleqtion", machine="cq_sqale_qpu")

# Run on Infleqtion Noisy Simulator
# cudaq.set_target("infleqtion", machine="cq_sqale_qpu", method=”noise-sim”)

# Sample kernel on specified backend
result = cudaq.sample(kernel)

Infleqtion’s Sqale neutral atom QPU, benchmarked in a recent preprint, optically traps and manipulates qubits in scalable and reconfigurable arrays of up to 1,600 qubits. Such reconfigurable systems provide flexibility for application co-design. The logically encoded materials science experiment used a triangular qubit array (Figure 3). This improved algorithm efficiency over a typical square lattice with just a few lines of code.  

Get started

Infleqtion’s breakthrough logical qubit demonstration was enabled by the versatility and performance of CUDA-Q. Now that CUDA-Q code can run on Infleqtion’s Sqale neutral atom QPU, it’s easier than ever to start building and accelerating logical qubit applications.

To get started, download CUDA-Q. See the full code for Infleqtion’s logical qubit demonstration, and begin implementing your own fault tolerant applications today. To learn more about other tools for enabling accelerated quantum supercomputing, visit NVIDIA Quantum.