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Our latest performance benchmarks with Ava.

Fidelity

By compressing the quantum state, Ava can scale (far) beyond the traditional statevector approach to large numbers of qubits.

 

How close the compressed state is to the ideal state is captured by the fidelity, which is controlled by the bond dimension that determines the amount of compression.

Performance

The performance of Ava depends heavily on the circuit. This is because Ava approximates the state of the quantum computer by a compressed state with limited entanglement. Therefore, the more entanglement generated by the circuit the more challenging it is for Ava.

 

How much entanglement a circuit builds up is difficult to say in advance – the best way to find out is simply to perform the emulation and see what fidelity can be obtained within a given computational budget.

Benchmarking

Benchmarking a statevector simulator is fairly straightforward: faster is better.

 

Benchmarking approximate emulators is a bit more nuanced. Is it better to obtain perfect fidelity in 1 hour than fidelity ½ in 10 minutes? What about fidelity 0.001 in 50 seconds? The answer will be use-case dependent, and the true test of an approximate emulator lies in applying it to real problems.

Benchmarks overview

Below is an overview of the benchmarks we have performed so far with Ava. We will add to this list as we run more benchmarks. Stay tuned!

Transverse-field Ising Model (TFIM)

The Ising model is a well-known and extensively studied model in condensed matter physics.

In this benchmark we emulate a quantum circuit implementing time-evolution with the Hamiltonian for the Ising model with a transverse magnetic field. This is a natural application of quantum computers: for them, time-evolution is 'easy', whereas simulating it classically is challenging because entanglement builds up in the state over time.

 

We find that fidelity 1 can only be achieved for shallow circuits, which correspond to short time scales, or for small numbers of qubits. By increasing the bond dimension, and leveraging GPU-acceleration, Ava manages to achieve good fidelity even for longer time scales and larger qubit numbers, whilst keeping the required computation time to a minimum.

(Full post coming soon!)

tfim_heatmap_fidelity.png

Quantum Fourier Transform (QFT)

The quantum Fourier transform is a standard building block for quantum algorithms, including phase estimation and period finding.

The QFT does not create much entanglement. Contrary to the transverse-field Ising model, it is relatively easy to emulate when acting on a state that is not very entangled. We find that Ava can obtain fidelity 1 on the QFT circuit using only a bond dimension of 32, for every number of qubits that we tested (up to 2000).

This benchmark is a clear example of a circuit for which Ava is capable of going far beyond the reach of conventional statevector simulators (which, even on the largest supercomputer cannot go beyond 50 qubits). It also demonstrates that Ava is capable of exploiting the limited entanglement-building properties of quantum circuits like the QFT without any fine-tuning. 

(Full post coming soon!)

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