Gaussian states are essential resources for diverse fields including quantum simulation and chemistry, yet preparing them efficiently on digital quantum computers presents a significant challenge. Yichen Xie from La Salle College and Nadav Ben-Ami from Classiq Technologies, along with their colleagues, now demonstrate a new circuit-based method for creating approximate Gaussian states with markedly reduced complexity. The team’s approach begins by shaping qubit amplitudes and then utilises a Fourier transform to generate the desired Gaussian profile, achieving high fidelity while minimising the number of necessary quantum gates. This innovation represents a crucial step towards making Gaussian states practical for near-term quantum devices and opens exciting possibilities for scalable quantum computations involving continuous-variable systems.
Researchers often select a Gaussian profile in their probability amplitudes. Although Gaussian states are natural in continuous-variable systems, the practical interest in digital, gate-based quantum computers demands discrete approximations of Gaussian distributions over a computational basis of size 2n. Because of the exponential scaling of naive amplitude-encoding approaches and the cost of certain block-encoding or Hamiltonian simulation techniques, a resource-efficient preparation of approximate Gaussian states is required.
Efficient Gaussian State Preparation with Qubits
Creating quantum states that follow a Gaussian distribution is crucial for many quantum algorithms used in areas like finance, machine learning, and simulating physical systems. This research addresses the challenge of representing continuous Gaussian distributions on quantum computers, which operate with discrete qubits, by introducing a new algorithm that efficiently approximates Gaussian states. The method begins by creating an exponential amplitude profile using single-qubit rotations, then employs the quantum Fourier transform to shape these amplitudes into a near-Gaussian form. A key innovation lies in selectively removing, or “pruning,” some of the operations within the quantum Fourier transform, drastically reducing the number of quantum gates needed and improving the algorithm’s scalability.
This gate reduction technique allows the algorithm to scale more efficiently with the number of qubits, approaching a near-linear relationship instead of the quadratic scaling common in traditional methods. The team demonstrates that this pruning process maintains high fidelity, ensuring the approximated Gaussian state remains accurate. This combination of efficiency and accuracy is critical for running complex simulations on real quantum hardware.
Efficient Gaussian State Preparation via Pruning
Researchers have developed a new method for creating approximate Gaussian states on quantum computers, which are crucial for simulating complex systems in fields like chemistry and materials science. Gaussian states, representing probability distributions with a characteristic bell curve, are naturally present in many physical systems, but difficult to represent accurately using the discrete nature of quantum bits, or qubits. This new approach efficiently prepares these states by initially creating an exponential amplitude profile using single-qubit rotations, then employing a modified Fourier transform to map those amplitudes into a Gaussian distribution. The key breakthrough lies in a technique to reduce the computational demands of this process.
By strategically removing, or “pruning,” small components of the Fourier transform, researchers significantly reduce the number of operations needed, scaling the gate complexity to near-linear with the number of qubits. This is a substantial improvement over traditional methods, which often require a number of operations that grows much faster. Testing demonstrates that this pruning process maintains high fidelity, a measure of how closely the created state matches the ideal Gaussian, with high fidelity achievable even with aggressive pruning. This combination of high fidelity and reduced gate complexity represents a significant step towards making Gaussian state preparation practical for larger and more complex quantum simulations.
Shaping Gaussian States with Simplified Quantum Circuits
This research presents a new circuit-based method for preparing approximate Gaussian states on digital quantum computers. The technique begins by creating an exponential amplitude profile using single-qubit rotations, then employs the quantum Fourier transform to shape these amplitudes into a near-Gaussian distribution. Importantly, the method allows for optional pruning of small controlled-phase angles within the Fourier transform, reducing the circuit’s complexity to near-linear scaling with the number of qubits. The results demonstrate that this approach achieves high fidelity in approximating Gaussian states while maintaining a relatively shallow circuit depth. Numerical simulations confirm the accuracy of the method, and preliminary tests on quantum hardware reveal a recognizable Gaussian peak structure, even with a limited number of qubits. This work offers a promising pathway toward scalable Gaussian state initialization, bridging the gap between theoretical requirements and practical implementation on current and future quantum devices.