Simple Diagonal State Designs with Reconfigurable Real-Time Circuits

Abstract

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.

References in corpus (21)

• Quantum algorithm for solving linear systems of equations
• Probing many-body dynamics on a 51-atom quantum simulator
• Predicting Many Properties of a Quantum System from Very Few Measurements
• On the Power of One Bit of Quantum Information
• Robust randomized benchmarking of quantum processes
• Exact and Approximate Unitary 2-Designs: Constructions and Applications
• Characterizing Quantum Gates via Randomized Benchmarking
• A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
• Evenly distributed unitaries: on the structure of unitary designs
• Randomizing quantum states: Constructions and applications
• Introduction to Haar Measure Tools in Quantum Information: A Beginner's Tutorial
• Fault-Tolerant Computing With Biased-Noise Superconducting Qubits
• Random phase vector for calculating the trace of a large matrix
• Efficient unitary designs with nearly time-independent Hamiltonian dynamics
• Measuring Arbitrary Physical Properties in Analog Quantum Simulation
• Quantum circuits for exact unitary $t$-designs and applications to higher-order randomized benchmarking
• Generating a state $t$-design by diagonal quantum circuits
• Shadow tomography from emergent state designs in analog quantum simulators
• Enhanced connectivity of quantum hardware with digital-analog control
• Hierarchical Clifford transformations to reduce entanglement in quantum chemistry wavefunctions
• Diagonal-unitary 2-designs and their implementations by quantum circuits