Session W14: Measurement-Induced Phase Transitions

Information exchange symmetry breaking in quantum-enhanced experiments

A quantum-enhanced experiment, in which quantum information is transduced from a system of interest and processed on a quantum computer, has the possibility of exponential advantage in sampling tasks over a traditional experiment, in which only the measurement outcomes of projec- tive or weak measurements are stored on a classical computer. In this work, we demonstrate that, similar to the measurement induced phase transition (MIPT) occurring in traditional experiments, quantum-enhanced experiments can also show entanglement phase transitions. We identify an in- formation exchange symmetry which is spontaneously broken both in the MIPT and in a class of quantum-enhanced experiments obeying this symmetry. The symmetry requires that the informa- tion recorded in the classical or quantum computer is as informative about the dynamics of the system as the information lost into the environment. We introduce a noisy transduction operation, and show that it satisfies this symmetry. The noisy transduction operation acts independently on two qubits, recording the quantum state of one qubit in the measurement apparatus, while erasing the quantum state of the other qubit with the environment. We then construct a random brickwork circuit which shows an entanglement transition tuned by the rate of noisy transduction operations. The symmetric phase of such transition is characterized by area law entanglement, where the sub- system entropy conditioned on the quantum states in the apparatus does not scale with system size, while the symmetry broken phase is characterized by volume law scaling entanglement. Our work introduces a quantum generalization of the MIPT entanglement transitions, and provides a unified framework to understand both as a spontaneous symmetry breaking of the information exchange symmetry.   

Boundary transfer matrix spectrum of measurement-induced transitions

Measurement-induced phase transitions (MIPTs) are known to be described by non-unitary conformal field theories (CFTs) whose precise nature remains unknown. Most physical quantities of interest, such as the entanglement features of quantum trajectories, are described by boundary observables in this CFT. We introduce a transfer matrix approach to study the boundary spectrum of this field theory, and consider a variety of boundary conditions. We apply this approach numerically to monitored Haar and Clifford circuits, and to the measurement-only Ising model where the boundary scaling dimensions can be derived analytically. Our transfer matrix approach provides a systematic numerical tool to study the spectrum of MIPTs.   

Random-matrix theory of measurement-induced phase transitions in nonlocal Floquet quantum circuits

Monitored quantum circuits and measurement-induced phase transitions (MIPTs) have attracted a lot attention as a result of the novel physics appearing due to the interplay of the unitary dynamics and measurements. In this work, we introduce and study a nonlocal monitored Floquet quantum circuit model that exhibits analytically treatable forced MIPT. We focus on spectral and dynamical signatures of the transition. Remarkably, we find a transition in the spectrum of the defect operator between the phase with and without a spectral gap.  In contrast to the measurement-induced transitions discussed in a number of previous works, the gap closing in the spectrum of this operator corresponds to physical observables that can be measured experimentally.   

Measurement-Induced Entanglement Phase Transitions in Constrained Hilbert Spaces

We explore the influence of Hilbert space constraints on the critical properties of measurement-induced phase transitions. Our investigation centers on the low-energy Hilbert space of the 1D PXP model, characterized by the constraint that adjacent states cannot be simultaneously excited. Notably, this constraint leads to a Hilbert space size growth as ~Φ^L instead of the typical ~2^L where Φ is the golden ratio and L is the number of qubits, rendering computational simulations less resource intensive. We study monitored random quantum circuits containing single-qubit Haar random gates (which are entangling by virtue of constraints) and projective measurements. We find compelling numerical evidence that the system undergoes a novel phase transition from area-law to volume-law entanglement as a function of the rate of projective measurements. Remarkably, we discover that the critical behavior of the entanglement transition belongs to a novel universality class, distinct from the behavior observed in Haar random circuits without the constraint. This underscores the profound influence of Hilbert space constraints on the system's dynamics. Hence, we comment on the implications of our results for measurement-induced phase transitions in lattice gauge theories and possibilities for experimental realization in Rydberg atom quantum simulators.   

Measurement-induced phase transitions in the toric code

We show how distinct phases of matter can be generated by performing random single-qubit measurements on a subsystem of toric code. Using a parton construction, such measurements map to random Gaussian tensor networks, and in particular, random Pauli measurements map to a classical loop model in which watermelon correlators precisely determine measurement-induced entanglement. Measuring all but a 1d boundary of qubits realizes hybrid circuits involving unitary gates and projective measurements in 1+1 dimensions. We find that varying the probabilities of different Pauli measurements can drive transitions in the un-measured boundary between phases with different orders and entanglement scaling, corresponding to short and long loop phases in the classical model. Furthermore, by utilizing single-site boundary unitaries conditioned on the bulk measurement outcomes, we generate mixed state ordered phases and transitions that can be experimentally diagnosed via linear observables. This demonstrates how parton constructions provide a natural framework for measurement-based quantum computing setups to produce and manipulate phases of matter. Looking ahead, our future directions envolves exploring the deeper connections between the universality of the resource state in MBQC and the entanglement patterns induced by measurement.   

Hierarchy of Symmetric Phases in Random Hybrid Quantum Circuits

Measurement-induced phase transitions are novel non-equilibrium phenomena that have yielded fruitful insights into the role of measurement in quantum information. Distinct phases reflect different ensembles of state entanglement structures emerging from individual trajectories through a quantum circuit. Of interest is the relationship between the properties of these phases and resource states considered in measurement-based quantum computing. The robustness of the latters' entanglement structures, which typically reflect (subsystem) topological symmetry, have been considered in a variety of ways in the past. Recently it was shown that the 1d cluster state belongs to a distinguishable phase in a random hybrid quantum circuit ensemble. The phase transition exhibits the same percolation universality as that occurring between generic unitary dynamics and measurements. To probe the sensitivity of the transition to the presence symmetry, we investigate the 2d cluster state for three different levels of symmetry-respecting unitary dynamics interspersed by measurements: arbitrary 5-qubit Clifford unitaries, symmetry-respecting-, and subsystem-symmetry respecting Cliffords. Our work on these random hybrid circuit models may have implications for hierarchies of transitions in computational power.   

Charge/Spin Sharpening Transition on Dynamical Quantum Trees

The dynamics of monitored quantum systems can generally be described by either a entangling phase where the initial information is protected by quantum scrambling and a disentangling phase where information is lost due to measurement. The transition between these two phases is so called the measurement induced phase transition. Recent work shows that the dynamics inside the entangling phase can be enriched by symmetries of quantum dynamics. However, although a random walk picture about Abelian sharpening transition has been established, the understanding about phase transitions with non-Abelian symmetry like SU(2) is still limited. In this work, we study the charge/spin sharpening in monitored dynamical quantum trees, which has more analytical trackabilities. We find that when the dynamics has U(1)/SU(2) symmetry, an extra transition can be defined based on whether the measurements can fully determine the final charge/spin or not, besides the usual entanglement transition critical point in previous work.   

Entanglement transitions in translation-invariant tensor networks

Recent studies of random tensor networks and quantum circuits led to the discovery of entanglement phase transitions in which the time evolving or boundary state changes from area law to volume law entanglement. In this work we explore the entanglement properties of the boundary state of a translationally invariant two dimensional tensor network, allowing us to use an infinite matrix product state approach to contract it row by row. Preliminary finite entanglement scaling analysis gives evidence for an entanglement transition that can be tuned either by (i) the virtual bond dimension (ii) the unitarity of the transfer matrix. Translational invariance means that row by row contraction defines an effective non unitary floquet evolution. Thus we conjecture that the entanglement transition is accompanied by a spectral transition of the transfer matrix akin to a transition to chaos.   

How Efficiently can Measurement Induce Entanglement?

It is known that measurements, despite being decohering processes, can teleport entanglement. A prime example is Bell teleportation. Such phenomena are not restricted to simple systems; they also manifest in many-body quantum states, termed as 'measurement-induced entanglement' (MIE). While MIE offers a potent method to investigate quantum systems, the efficiency of its generation remains unknown. Specifically, it's unclear how many bits need to be measured to produce a given amount of bits of entanglement. In this work, we establish a strict upper bound on the efficiency of MIE generation: an increase of at most one bit of MIE per bit of measurement, saturated by Bell teleportation. Alongside this proof, we introduce a framework for characterizing MIE using quantum conditional mutual information. This novel approach not only builds upon existing definitions but also distinguishes classical correlations from MIE. To understand concrete examples, we explore the efficiency of MIE generation in states prepared by random unitary circuits. Our numerical analyses reveal that circuits with greater depth produce MIE more efficiently. We explain this relationship through the statistical mechanics model.   

Measurement-Induced Phase Transition in the Classical Simulability of Random Clifford+T Circuits

Classical simulations of quantum systems are conjectured to be generically inefficient, particularly when the system is highly entangled. Recently discovered "measurement-induced phase transitions" in entanglement suggest a corresponding phase transition in the classical simulability of quantum systems. However, some entanglement-generating quantum (such as Clifford) circuits are nevertheless simple to classically simulate, suggesting a more nuanced treatment of simulability is required. Here, we find a phase transition in the simulability of random quantum circuits composed of Clifford gates, T gates and measurements. The transition is related to the amount of "magic" in the circuit—another quantum resource distinct from entanglement—that is related to the number of T gates and distribution of measurements in the circuit. We put forward "stabilizer-purification"—a process by which measurements collapse a superposition of stabilizer states to a single one—as the mechanism driving this simulability phase transition.   

Learnability transitions in monitored quantum dynamics via eavesdropper's classical shadows

The dynamics of quantum many-body systems subject to repeated measurements has recently emerged as a rich subject for non-equilibrium physics. Remarkably, these systems can exhibit "measurement-induced phase transitions" (MIPTs) in the structure of quantum correlations, such as entanglement, as a function of the rate or strength of measurements versus unitary interactions. We present an alternative point of view on these phenomena, based not on the structure of correlations in post-measurement states of the quantum system, but rather on the information content of the measurement outcomes themselves. The MIPT maps onto a phase transition in the ability of an eavesdropper to learn properties of an unknown state of the system by monitoring its dynamics. This learnability phase transition can be quantified within the framework of "classical shadow tomography"--a paradigm for learning many properties of quantum states from randomized measurements--where it arises as an abrupt change in the number of experimental repetitions required to learn various properties. This point of view unifies distinct manifestations of the MIPT under a common denominator, and points to new order parameters that could be used for its experimental detection.   

Interplay of measurement and control induced phase transitions in β-adic Rényi circuits

Developing a general understanding of phase transitions far from equilibrium remains a pressing open question in quantum statistical mechanics. Recently, a great deal of attention has focused on measurement-induced phase transitions (MIPT) in the entanglement of the quantum state that occurs due to the competition between entangling unitary dynamics and disentangling random local measurements. Incorporating feedback from the measurement outcome can steer the dynamics to a predetermined final unentangled state, but only after a critical rate of feedback has been applied, defining control-induced phase transitions (CIPTs). The interplay of the MIPT and the CIPT is studied in a variety of Haar random quantum circuits derived from β-adic Rényi maps with different control protocols to understand what details dictate the overall topology of the phase diagram. Several computational approaches are used, and their efficiency will be discussed in detail.   

Absorbing Phases in Adaptive Circuits

I will discuss the construction of specific target states in 1D quantum circuits using measurements followed by outcome-dependent feedback. There is a critical rate of measurement above which these protocols can be successful, but symmetries can impact their viability. By studying two families of models - qubits undergoing unitary evolution with a special structure, and free fermions - a Z2 symmetry is found to slow the preparation of such states. This is explained by a mapping to Branching-Annihilating Random Walks.   

Realizing measurement-induced phase transitions in multimode circuit QED systems

Multimode microwave cavities with ultra-low losses have been combined with superconducting circuits to realize a novel platform for quantum information processing and quantum simulations with bosons. This platform leverages interactions of the superconducting circuit with the cavity modes to implement multimode bosonic quantum circuits interspersed with local measurements (such as parity or the photon number operator). This allows for interesting hybrid dynamics and the possibility of studying measurement-induced entanglement phase transitions (MIPT) in a multi-qudit system in the presence of conserved quantities. We will present theoretical results showing signatures of MIPT in this system in various ancilla based order parameters. We will also explore the feasibility of observing this transition in experiments featuring a 3D circuit QED device where a Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL) interfaces a multimode cavity to a separate few-mode buffer cavity, in turn integrated with a separate transmon ancilla. This system allows for the implementation of fast beam-splitter gates between any pair of cavity modes via 3-wave mixing, as well as high-fidelity measurements on individual modes using the transmon ancilla.   

Robust measurement-induced phase transitions and observables in noisy dynamics

Measurement-induced phase transitions generally suffer from two problems: fragility to noise and reliance on exponentially-costly postselection to be observed. Here, we seek to address both of these issues in a (2+1)d measurement-only model inspired by the toric code. We find noise-robust measurement-induced transitions in topological negativity and in purification timescales. Although these transitions rely on postselection, we study the performance of linear cross-entropy (LXE) as an efficiently-computable observable. Without modification, the LXE fails to show a phase transition in the presence of noise. However, we show how measurement results can be decoded to yield a robust LXE in certain regions of our phase diagram and we explore the theoretical limitations on this decoding.