Simple Diagonal State Designs with Reconfigurable Real-Time Circuits
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917205244903424 |
|---|---|
| author | Shen, Yizhi Klymko, Katherine Rabani, Eran Tubman, Norm M. Camps, Daan Van Beeumen, Roel Lindsey, Michael |
| author_facet | Shen, Yizhi Klymko, Katherine Rabani, Eran Tubman, Norm M. Camps, Daan Van Beeumen, Roel Lindsey, Michael |
| contents | Unitary designs are widely used in quantum computation, but in many practical settings it suffices to construct a diagonal state design generated with unitary gates diagonal in the computational basis. In this work, we introduce a simple and efficient diagonal state 3-design based on real-time evolutions under 2-local Hamiltonians. Our construction is inspired by the classical Girard-Hutchinson trace estimator in that it involves the stochastic preparation of many random-phase states. Though the exact Girard-Hutchinson states are not tractably implementable on a quantum computer, we can construct states that match the statistical moments of the Girard-Hutchinson states with real-time evolution. Importantly, our random states are all generated using the same Hamiltonians for real-time evolution, with the randomness arising solely from stochastic variations in the durations of the evolutions. In this sense, the circuit is fully reconfigurable and thus suited for near-term realizations on both digital and analog platforms. Moreover, we show how to extend our construction to achieve diagonal state designs of arbitrarily high order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04176 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simple Diagonal State Designs with Reconfigurable Real-Time Circuits Shen, Yizhi Klymko, Katherine Rabani, Eran Tubman, Norm M. Camps, Daan Van Beeumen, Roel Lindsey, Michael Quantum Physics Unitary designs are widely used in quantum computation, but in many practical settings it suffices to construct a diagonal state design generated with unitary gates diagonal in the computational basis. In this work, we introduce a simple and efficient diagonal state 3-design based on real-time evolutions under 2-local Hamiltonians. Our construction is inspired by the classical Girard-Hutchinson trace estimator in that it involves the stochastic preparation of many random-phase states. Though the exact Girard-Hutchinson states are not tractably implementable on a quantum computer, we can construct states that match the statistical moments of the Girard-Hutchinson states with real-time evolution. Importantly, our random states are all generated using the same Hamiltonians for real-time evolution, with the randomness arising solely from stochastic variations in the durations of the evolutions. In this sense, the circuit is fully reconfigurable and thus suited for near-term realizations on both digital and analog platforms. Moreover, we show how to extend our construction to achieve diagonal state designs of arbitrarily high order. |
| title | Simple Diagonal State Designs with Reconfigurable Real-Time Circuits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2401.04176 |