isaacdevlugt
commented
2 years ago Thank you for your Power Up submission! As a reminder, the final deadline for your project is February 25 at 17h00 EST. Submissions should be done here: https://github.com/XanaduAI/QHack/issues/new?assignees=&labels=&template=open_hackathon.md&title=%5BENTRY%5D+Your+Project+Title
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Team Name:
Marpeq
Project Description:
Our project aims to implement the recent suggestion by Rahmani et al. to simulate the Laughlin wavefunction of the ⅓ FQH state. This suggestion takes advantage of a clever reduction of the 2D state to a 1D system. We plan to implement and execute a circuit, verify it yields the required quantum state, and measure interesting physical properties such as the mutual statistics of quasi-particles. Since current NISQ devices are small and scarcely available, we also intend to implement a pennylane version of the parallelization system proposed by Barrat. The system allows simulations of large systems using only a handful of qubits. Since the FQH state is topologically ordered, we cannot rely on measurements of a local order parameter to verify the circuit generates the intended state. Thus it necessitates the measurement of non-local string operators. This means we must extend Barrat’s algorithm to facilitate measurements of non-local operators. We believe this is possible because the FQH ground state assumes the form of a matrix product state.
One challenging issue we need to face in order to complete our plan is the mitigation of noise. Beyond the inherent noise that inflicts each qubit during each gate application Rahmani et al.’s suggestion assumes a snake-like connectivity topology of the qubits in order to use nearest-neighbor two-qubits. Since the device does not provide such connectivity, the noise is amplified by the requirement to execute additional SWAP gates. These allow the device to provide the connectivity between far away qubits. To overcome this issue, we will use simulator measurements of Rahmani et al.’s idealized circuit as training data for a variational circuit. The parameters of the variational circuit will be optimized to yield the FQH state.
Source code:
https://github.com/ShapeshiftingMasterOfDarkness/QHack2022-FQHE
Resource Estimate:
The circuit we will implement acts on 3-qubit blocks. Suppression of boundary effects requires about 22 qubits as Rahmani et al. estimates. Currently the teams’ computers are barely able to simulate such a system, and to properly measure on larger systems (with enough measurement for precise and accurate results) is almost impossible. We will use the AWS credits to run on the SV1 simulator and the Rigetti Aspen-11 device. We will simulate a 30 qubits system for 200 shots each time, to perform 4 physical experiments (2 kinds of correlation function, a string order parameter, quasi-particle mutual statistics). We will also train a variational circuit, which will require several dozen tasks with a similar number of shots each, time several iterations.
Together with our parallelization scheme, we could accelerate the simulation and obtain more accurate and reliable measurements of more exciting and complicated physical processes. For a system of N qubits simulated over d actual qubits, we will need to run O(N/d) measurement cycles. Since the circuit size is linear in the number d of qubits we expect the execution to be fast. So O(dN/d)=O(N) cycles in total are needed for the parallelization system.