Exact answers, provable bounds.

What we do

Exact results for problems at the frontier of quantum computing.

We deliver software solutions to some of the biggest challenges in making quantum computers useful. Our tools provide mathematically exact answers in domains of exponential complexity: How to simulate a quantum computation with classical resources as fast as possible? How to use quantum-HPC resources as efficiently as possible? How to optimally distribute quantum circuits between different QPUs of limited capacity?

Alternative simulation tools are not guaranteed to be close to optimal strategies. Our software (patent filed) is the first to carry out these tasks with performance guarantees - usually beating alternative methods or landing on the mathematical optimum.

Use cases

Classical simulations

Network flow diagram converging into software

Hybrid quantum computing

HPC racks exchanging data with a quantum processor

Distributed quantum computing

Three quantum processors linked in a glowing network
Example

The question of quantum supremacy.

The lower and upper bounds on classical simulation costs provided by our tools can be used to settle questions around quantum supremacy. Specifically, one can bound how many floating point operations (FLOPs) are needed to contract a given quantum circuit exactly. If the lower bound exceeds a given budget (e.g., one second on Frontier, one hour on Frontier), we call the corresponding quantum processor quantum supreme. The two figures below show the lower bound and upper bound obtained using our software for the Google Sycamore processor and their more recent Willow processor as a function of the number of cycles.

FLOP count versus number of cycles for simulating the Sycamore processor, with Cotengra estimates, upper and lower bounds, and the quantum supremacy limit
FLOP count required to simulate one amplitude of the Google Sycamore processor as a function of the number of cycles, with upper and lower bounds provided by our tool. For comparison, we show the optimal contraction complexity obtained with Cotengra run for approximately the same time as our software. The dotted line corresponds to the peak performance of Frontier over one second (1.71 exaFLOPs).
FLOP count versus number of cycles for simulating the Willow processor, with Cotengra estimates, bounds, and Frontier compute-time reference lines
FLOP count required to simulate one amplitude of the Google Willow processor as a function of the number of cycles, with upper and lower bounds provided by our tool and Cotengra results shown for comparison. The dotted line corresponds to Frontier's peak performance over one second and the dashed line to one hour at an average efficiency of 20%.

These results can be used to chart the quantum supremacy diagram of superconducting quantum processors of the Sycamore-Willow architecture below. The diagram consists of a provably classically simulable regime, where our upper bound sits below the computational budget of one Frontier second and a quantum supreme regime, where even the lower bound exceeds the designated computational budget, separated by a narrow grey zone. While the set computational budget is arbitrary, redefining it only shifts the quantum supremacy boundary marginally (cf. orange crosses corresponding to one Frontier hour at 20% efficiency). We note that either way, the Willow processor with 40 cycles of operation is located deep in the quantum supremacy regime.

Phase diagram of number of cycles versus number of qubits separating the classically simulable region from the quantum supreme region, with Sycamore and Willow experiments marked
Quantum supremacy diagram. The red crosses are located at maximum number of cycles that can be executed with the corresponding processors.