[Paper Review] Observation of measurement-induced quantum phases in a trapped-ion quantum computer

Crystal Noel, Pradeep Niroula+9 more|arXiv (Cornell University)|Jun 10, 2021

Quantum Computing Algorithms and Architecture30 references24 citations

TL;DR

Demonstrates experimentally the purification (pure) and coding (mixed) phases in measurement-induced transitions using a trapped-ion quantum computer, with evidence of the two phases and initial critical behavior via reference-qubit entropy measurements.

ABSTRACT

Many-body open quantum systems balance internal dynamics against decoherence from interactions with an environment. Here, we explore this balance via random quantum circuits implemented on a trapped ion quantum computer, where the system evolution is represented by unitary gates with interspersed projective measurements. As the measurement rate is varied, a purification phase transition is predicted to emerge at a critical point akin to a fault-tolerent threshold. We probe the "pure" phase, where the system is rapidly projected to a deterministic state conditioned on the measurement outcomes, and the "mixed" or "coding" phase, where the initial state becomes partially encoded into a quantum error correcting codespace. We find convincing evidence of the two phases and show numerically that, with modest system scaling, critical properties of the transition clearly emerge.

Motivation & Objective

• Motivate and realize measurement-induced phase transitions in monitored quantum many-body dynamics.
• Distinguish the pure (rapidly projected) and mixed/coding (codespace-preserving) phases using a reference qubit as an order parameter.
• Show experimental evidence for the two phases with modest system sizes and discuss scaling toward universal critical behavior.
• Explore how feedback and measurement strategies enable scalable probing without post-selection.

Proposed method

• Implement random quantum circuits with unitary gates and interspersed projective measurements on up to 13 Yb-171 ions in a 15-ion chain.
• Use a reference qubit entangled with the system to test for the existence of a codespace in the mixed phase and its absence in the pure phase.
• Employ a scrambling unitary followed by random XX(pi/4) gates and probabilistic mid-circuit measurements to realize purification dynamics.
• Measure the reference qubit entropy S_Q by performing tomography in X, Y, Z bases and post-select via a feedback-based disentangling circuit to obtain a classical entropy S_C.
• Append a classical feedback circuit to disentangle the reference from measurement ancillae, enabling thresholding of S_C without post-selection.
• Analyze ensembles of random circuits at fixed p=0.15 and varying p_x and L to construct phase diagrams and perform finite-size scaling to extract critical behavior.

Experimental results

Research questions

• RQ1 Do measurement-induced purification and coding phases emerge in a trapped-ion circuit with random unitary dynamics and measurements?
• RQ2 Can a single reference qubit reveal the presence or absence of a codespace characteristic of the mixed vs. pure phase, respectively?
• RQ3 What are the finite-size signatures and scaling behaviors near the purification transition in all-to-all coupled random circuits?
• RQ4 How does introducing x-basis measurements (p_x) affect the purification transition and its universality class?
• RQ5 Are the observed critical properties (e.g., dynamic exponent) accessible with near-term ion-trap hardware and modest system sizes?

Key findings

• Evidence for both mixed/coding and pure phases in the purification transition, observed via reference-qubit entropy behavior and thresholded classical entropy S_C.
• Phase diagram shows mixed phase at low p and p_x and pure phase at higher p_x or p, with a critical point p_xc≈0.72(1) at p=0.15 in simulations; experimental data for L≤8 show phase separation consistent with simulations.
• Finite-size scaling suggests late-time decay τ of S_Q scales as L^{z} with z≈1/5 near criticality, compatible with mean-field percolation expectations for this all-to-all setting.
• An experimentally scalable approach using feedback disentangling of the reference qubit avoids post-selection and reduces resource needs, enabling direct observation of the two phases.
• Noisier simulations including XX-gate crosstalk and dephasing account for higher observed entropies, yet clear separation between mixed and pure regimes persists for small system sizes (L=4,6).
• Critical properties identified (z≈1/5, ν≈1/2) are consistent with percolation-based expectations, with plans to scale to larger systems (L up to 32) and use sympathetic cooling to access deeper critical behavior.