URL: Quantum Journal

Quantum Journal News

Tuesday, July 29, 2025

• Dual-unitary shadow tomography
  

  Quantum 9, 1816 (2025).

  https://doi.org/10.22331/q-2025-07-29-1816

  We introduce “dual-unitary shadow tomography'' (DUST), a classical shadow tomography protocol based on dual-unitary brick-wall circuits. To quantify the performance of DUST, we study operator spreading and Pauli weight dynamics in one-dimensional qubit systems, evolved by random two-local dual-unitary gates arranged in a brick-wall structure, ending with a measurement layer. We do this by deriving general constraints on the Pauli weight transfer matrix and specializing to the case of dual-unitarity. Remarkably, we find that operator spreading in these circuits have a rich structure resembling that of relativistic quantum field theories, with massless chiral excitations that can decay or fuse into each other, which we call left- or right-movers. We develop a mean-field description of the Pauli weight in terms of $\rho(x,t)$, which represents the probability of having nontrivial support at site $x$ and depth $t$ starting from a fixed weight distribution. We develop an equation of state for $\rho(x,t)$ and simulate it numerically using Monte Carlo simulations. For the task of predicting operators with (nearly) full support, we show that DUST outperforms brick-wall Clifford shadows of equal depth. This advantage is further pronounced for small system sizes and our results are generally robust to finite-size effects.

  
  
• Conservation Laws For Every Quantum Measurement Outcome
  

  Quantum 9, 1815 (2025).

  https://doi.org/10.22331/q-2025-07-29-1815

  In the paradigmatic example of quantum measurements, whenever one measures a system which starts in a superposition of two states of a conserved quantity, it jumps to one of the two states, implying different final values for the quantity that should have been conserved. The standard law of conservation for quantum mechanics handles this jump by stating only that the total distribution of the conserved quantity over repeated measurements is unchanged, but states nothing about individual cases. Here however we show that one can go beyond this and have conservation in each individual instance. We made our arguments in the case of angular momentum of a particle on a circle, where many technicalities simplify, and bring arguments to show that this holds in full generality. Hence we argue that the conservation law in quantum mechanics should be rewritten, to go beyond its hitherto statistical formulation, to state that the total of a conserved quantity is unchanged in every individual measurement outcome. As a further crucial element, we show that conservation can be localised at the level of the system of interest and its relevant frame of reference, and is independent on any assumptions on the distribution of the conserved quantity over the entire universe.

  
  
• Exact Model Reduction for Continuous-Time Open Quantum Dynamics
  

  Quantum 9, 1814 (2025).

  https://doi.org/10.22331/q-2025-07-29-1814

  We consider finite-dimensional many-body quantum systems described by time-independent Hamiltonians and Markovian master equations, and present a systematic method for constructing smaller-dimensional, reduced models that $exactly$ reproduce the time evolution of a set of initial conditions or observables of interest. Our approach exploits Krylov operator spaces and their extension to operator algebras, and may be used to obtain reduced linear models of minimal dimension, well-suited for simulation on classical computers, or reduced quantum models that preserve the structural constraints of physically admissible quantum dynamics, as required for simulation on quantum computers. Notably, we prove that the reduced quantum-dynamical generator is still in Lindblad form. By introducing a new type of $\textit{observable-dependent symmetries}$, we show that our method provides a non-trivial generalization of techniques that leverage symmetries, unlocking new reduction opportunities. We quantitatively benchmark our method on paradigmatic open many-body systems of relevance to condensed-matter and quantum-information physics. In particular, we demonstrate how our reduced models can quantitatively describe decoherence dynamics in central-spin systems coupled to structured environments, magnetization transport in boundary-driven dissipative spin chains, and unwanted error dynamics on information encoded in a noiseless quantum code.

  
  
• Quantum Learning Theory Beyond Batch Binary Classification
  

  Quantum 9, 1813 (2025).

  https://doi.org/10.22331/q-2025-07-29-1813

  Arunachalam and de Wolf (2018) [1] showed that the sample complexity of quantum batch learning of boolean functions, in the realizable and agnostic settings, has the $\textit{same form and order}$ as the corresponding classical sample complexities. In this paper, we extend this, ostensibly surprising, message to batch multiclass learning, online boolean learning, and online multiclass learning. For our online learning results, we first consider an adaptive adversary variant of the classical model of Dawid and Tewari (2022) [2]. Then, we introduce the first (to the best of our knowledge) model of online learning with quantum examples.

  A poster (presented at QIP 2024) is hosted at the following GitHub permalink.

  
  

Wednesday, July 23, 2025

• Low variance estimations of many observables with tensor networks and informationally-complete measurements
  

  Quantum 9, 1812 (2025).

  https://doi.org/10.22331/q-2025-07-23-1812

  Accurately estimating the properties of quantum systems is a central challenge in quantum computing and quantum information. We propose a method to obtain unbiased estimators of multiple observables with low statistical error by post-processing informationally complete measurements using tensor networks. Compared to other observable estimation protocols based on classical shadows and measurement frames, our approach offers several advantages: (i) it can be optimised to provide lower statistical error, resulting in a reduced measurement budget to achieve a specified estimation precision; (ii) it scales to a large number of qubits due to the tensor network structure; (iii) it can be applied to any measurement protocol with measurement operators that have an efficient tensor-network representation. We benchmark the method through various numerical examples, including spin and chemical systems, and show that our method can provide statistical error that are orders of magnitude lower than the ones given by classical shadows.

  
  
• Experiments with Schrödinger Cellular Automata
  

  Quantum 9, 1811 (2025).

  https://doi.org/10.22331/q-2025-07-23-1811

  We derive a class of cellular automata for the Schrödinger Hamiltonian, including scalar and vector potentials. It is based on a multi-split of the Hamiltonian, resulting in a multi-step unitary evolution operator in discrete time and space. Experiments with one-dimensional automata offer quantitative insight in phase and group velocities, energy levels, related approximation errors, and the evolution of a time-dependent harmonic oscilator. The apparent effects of spatial waveform aliasing are intriguing. Interference experiments with two-dimensional automata include refraction, Davisson-Germer, Mach-Zehnder, single & double slit, and Aharonov-Bohm.

  Experiments with Schrödinger Cellular Automata.

     
  
  
• Circuit-level fault tolerance of cat codes
  

  Quantum 9, 1810 (2025).

  https://doi.org/10.22331/q-2025-07-23-1810

  Bosonic codes encode quantum information into a single infinite-dimensional physical system endowed with error correction capabilities. This reduces the need for complex management of many physical constituents compared with standard approaches employing multiple physical qubits. Recent discussions of bosonic codes centre around correcting only boson-loss errors, with phase errors either actively suppressed or deferred to subsequent layers of encoding with standard qubit codes. Rotationally symmetric bosonic (RSB) codes, which include the well-known cat and binomial codes, are capable of simultaneous correction of loss and phase errors, offering an alternate route that deals with arbitrary errors already at the base layer. Here, we investigate the robustness of such codes, moving away from the more idealistic past studies towards a circuit-level noise analysis closer to the practical situation where every physical component in the device is potentially faulty. We extend the concept of fault tolerance to the case of RSB codes, and then examine the performance of two known error correction circuits under circuit-level noise. Our analysis reveals a significantly more stringent noise threshold for fault-tolerant operation than found in past works; nevertheless, we show how, through waiting-time optimization and the use of squeezing, we can restore the noise requirements to a regime achievable with near-term quantum hardware. While our focus here is on cat codes for concreteness, a similar analysis applies for general RSB codes.

  
  
• Graphical Framework for Non-Gaussian Quantum States
  

  Quantum 9, 1809 (2025).

  https://doi.org/10.22331/q-2025-07-23-1809

  We provide a graphical method to describe and analyze non-Gaussian quantum states using a hypergraph framework. These states are pivotal resources for quantum computing, communication, and metrology, but their characterization is hindered by their complex high-order correlations. The framework encapsulates transformation rules for a series of typical Gaussian unitary operation and local quadrature measurement, offering a visually intuitive tool for manipulating such states through experimentally feasible pathways. Notably, we develop methods for the generation of complex hypergraph states with more or higher-order hyperedges from simple structures through Gaussian operations only, facilitated by our graphical rules. We present illustrative examples on the preparation of non-Gaussian states rooted in these graph-based formalisms, revealing their potential to advance continuous-variable general quantum computing capabilities.

  
  

Tuesday, July 22, 2025

• Critical spin models from holographic disorder
  

  Quantum 9, 1808 (2025).

  https://doi.org/10.22331/q-2025-07-22-1808

  Discrete models of holographic dualities, typically modeled by tensor networks on hyperbolic tilings, produce quantum states with a characteristic quasiperiodic disorder not present in continuum holography. In this work, we study the behavior of XXZ spin chains with such symmetries, showing that lessons learned from previous non-interacting (matchgate) tensor networks generalize to more generic Hamiltonians under holographic disorder: While the disorder breaks translation invariance, site-averaged correlations and entanglement of the disorder-free critical phase are preserved at a plateau of nonzero disorder even at large system sizes. In particular, we show numerically that the entanglement entropy curves in this disordered phase follow the expected scaling of a conformal field theory (CFT) in the continuum limit. This property is shown to be non-generic for other types of quasiperiodic disorder, only appearing when our boundary disorder ansatz is described by a "dual" bulk hyperbolic tiling. Our results therefore suggest the existence of a whole class of critical phases whose symmetries are derived from models of discrete holography.

  
  
• Certifying nonlocal properties of noisy quantum operations
  

  Quantum 9, 1807 (2025).

  https://doi.org/10.22331/q-2025-07-22-1807

  Certifying quantum properties from the probability distributions they induce is an important task for several purposes. While this framework has been largely explored and used for quantum states, its extrapolation to the level of channels started recently in a variety of approaches. In particular, little is known about to what extent noise can spoil certification methods for channels. In this work we provide a unified methodology to certify nonlocal properties of quantum channels from the correlations obtained in prepare-and-measurement protocols: our approach gathers fully and semi-device-independent existing methods for this purpose, and extends them to new certification criteria. In addition, the effect of different models of dephasing noise is analysed. Some noise models are shown to generate nonlocality and entanglement in special cases. In the extreme case of complete dephasing, the measurement protocols discussed yield particularly simple tests to certify nonlocality, which can be obtained from known criteria by fixing the dephasing basis. These are based on the relations between bipartite quantum channels and their classical analogues: bipartite stochastic matrices defining conditional distributions.

  
  
• The Cramér-Rao approach and global quantum estimation of bosonic states
  

  Quantum 9, 1806 (2025).

  https://doi.org/10.22331/q-2025-07-22-1806

  Quantum state estimation is a fundamental task in quantum information theory, where one estimates real parameters continuously embedded in a family of quantum states. In the theory of quantum state estimation, the widely used Cramér Rao approach which considers local estimation gives the ultimate precision bound of quantum state estimation in terms of the quantum Fisher information. However practical scenarios need not offer much prior information about the parameters to be estimated, and the local estimation setting need not apply. In general, it is unclear whether the Cramér-Rao approach is applicable for global estimation instead of local estimation. In this paper, we find situations where the Cramér-Rao approach does and does not work for quantum state estimation problems involving a family of bosonic states in a non-IID setting, where we only use one copy of the bosonic quantum state in the large number of bosons setting. Our result highlights the importance of caution when using the results of the Cramér-Rao approach to extrapolate to the global estimation setting.

  
  
• Dictionary-based Block Encoding of Sparse Matrices with Low Subnormalization and Circuit Depth
  

  Quantum 9, 1805 (2025).

  https://doi.org/10.22331/q-2025-07-22-1805

  Block encoding severs as an important data input model in quantum algorithms, enabling quantum computers to simulate non-unitary operators effectively. In this paper, we propose an efficient block-encoding protocol for sparse matrices based on a novel data structure, called the dictionary data structure, which classifies all non-zero elements according to their values and indices. Non-zero elements with the same values, lacking common column and row indices, belong to the same classification in our block-encoding protocol's dictionary. When compiled into the $\textit{{U(2), CNOT}}$ gate set, the protocol queries a $2^n \times 2^n$ sparse matrix with $s$ non-zero elements at a circuit depth of $\mathcal{O}(\log(ns))$, utilizing $\mathcal{O}(n^2s)$ ancillary qubits. This offers an exponential improvement in circuit depth relative to the number of system qubits, compared to existing methods [1,2] with a circuit depth of $\mathcal{O}(n)$. Moreover, in our protocol, the subnormalization, a scaled factor that influences the measurement probability of ancillary qubits, is minimized to $\sum_{l=0}^{s_0}\vert A_l\vert$, where $s_0$ denotes the number of classifications in the dictionary and $A_l$ represents the value of the $l$-th classification. Furthermore, we show that our protocol connects to linear combinations of unitaries (LCU) and the sparse access input model (SAIM). To demonstrate the practical utility of our approach, we provide several applications, including Laplacian matrices in graph problems and discrete differential operators.

  
  
• Bounds on Autonomous Quantum Error Correction
  

  Quantum 9, 1804 (2025).

  https://doi.org/10.22331/q-2025-07-22-1804

  Autonomous quantum memories are a way to passively protect quantum information using engineered dissipation that creates an “always-on'' decoder. We analyze Markovian autonomous decoders that can be implemented with a wide range of qubit and bosonic error-correcting codes, and derive several upper bounds and a lower bound on the logical error rate in terms of correction and noise rates. These bounds suggest that, in general, there is always a correction rate, possibly size-dependent, above which autonomous memories exhibit arbitrarily long coherence times. For any given autonomous memory, size dependence of this correction rate is difficult to rule out: we point to common scenarios where autonomous decoders that stochastically implement active error correction must operate at rates that grow with code size. For codes with a threshold, we show that it is possible to achieve faster-than-polynomial decay of the logical error rate with code size by using superlogarithmic scaling of the correction rate. We illustrate our results with several examples. One example is an exactly solvable global dissipative toric code model that can achieve an effective logical error rate that decreases exponentially with the linear lattice size, provided that the recovery rate grows proportionally with the linear lattice size.

  
  
• Neural Projected Quantum Dynamics: a systematic study
  

  Quantum 9, 1803 (2025).

  https://doi.org/10.22331/q-2025-07-22-1803

  We investigate the challenge of classical simulation of unitary quantum dynamics with variational Monte Carlo approaches, addressing the instabilities and high computational demands of existing methods. By systematically analyzing the convergence of stochastic infidelity optimizations, examining the variance properties of key stochastic estimators, and evaluating the error scaling of multiple dynamical discretization schemes, we provide a thorough formalization and significant improvements to the projected time-dependent Variational Monte Carlo (p-tVMC) method. We benchmark our approach on a two-dimensional Ising quench, achieving state-of-the-art performance. This work establishes p-tVMC as a powerful framework for simulating the dynamics of large-scale two-dimensional quantum systems, surpassing alternative VMC strategies on the investigated benchmark problems.

  NeuralQXLab / ptvmc-systematic-study at GitHub

  
  
• Symmetry verification for noisy quantum simulations of non-Abelian lattice gauge theories
  

  Quantum 9, 1802 (2025).

  https://doi.org/10.22331/q-2025-07-22-1802

  Non-Abelian gauge theories underlie our understanding of fundamental forces of modern physics. Simulating them on quantum hardware is an outstanding challenge in the rapidly evolving field of quantum simulation. A key prerequisite is the protection of local gauge symmetries against errors that, if unchecked, would lead to unphysical results. While an extensive toolkit devoted to identifying, mitigating, and ultimately correcting such errors has been developed for Abelian groups, non-commuting symmetry operators complicate the implementation of similar schemes in non-Abelian theories. Here, we discuss two techniques for error mitigation through symmetry verification, tailored for non-Abelian lattice gauge theories implemented in noisy qudit hardware: dynamical post-selection (DPS), based on mid-circuit measurements without active feedback, and post-processed symmetry verification (PSV), which combines measurements of correlations between target observables and gauge transformations. We illustrate both approaches for the discrete non-Abelian group $D_3$ in 2+1 dimensions, explaining their usefulness for current NISQ devices even in the presence of fast fluctuating noise. Our results open new avenues for robust quantum simulation of non-Abelian gauge theories, for further development of error-mitigation techniques, and for measurement-based control methods in qudit platforms.

  
  

Monday, July 21, 2025

• Probing quantum complexity via universal saturation of stabilizer entropies
  

  Quantum 9, 1801 (2025).

  https://doi.org/10.22331/q-2025-07-21-1801

  Nonstabilizerness or `magic' is a key resource for quantum computing and a necessary condition for quantum advantage. Non-Clifford operations turn stabilizer states into resourceful states, where the amount of nonstabilizerness is quantified by resource measures such as stabilizer Rényi entropies (SREs). Here, we show that SREs saturate their maximum value at a critical number of non-Clifford operations. Close to the critical point SREs show universal behavior. Remarkably, the derivative of the SRE crosses at the same point independent of the number of qubits and can be rescaled onto a single curve. We find that the critical point depends non-trivially on Rényi index $\alpha$. For random Clifford circuits doped with T-gates, the critical T-gate density scales independently of $\alpha$. In contrast, for random Hamiltonian evolution, the critical time scales linearly with qubit number for $\alpha$ $\gt$$1$, while it is a constant for $\alpha$$\lt$$1$. This highlights that $\alpha$-SREs reveal fundamentally different aspects of nonstabilizerness depending on $\alpha$: $\alpha$-SREs with $\alpha$$\lt$$1$ relate to Clifford simulation complexity, while $\alpha$$\gt$$1$ probe the distance to the closest stabilizer state and approximate state certification cost via Pauli measurements. As technical contributions, we observe that the Pauli spectrum of random evolution can be approximated by two highly concentrated peaks which allows us to compute its SRE. Further, we introduce a class of random evolution that can be expressed as random Clifford circuits and rotations, where we provide its exact SRE. Our results opens up new approaches to characterize the complexity of quantum systems.

  
  
• Averaging gate approximation error and performance of Unitary Coupled Cluster ansatz in Pre-FTQC Era
  

  Quantum 9, 1800 (2025).

  https://doi.org/10.22331/q-2025-07-21-1800

  Fault-tolerant quantum computation (FTQC) is essential to implement quantum algorithms in a noise-resilient way, and thus to enjoy advantages of quantum computers even with presence of noise. In FTQC, a quantum circuit is decomposed into universal gates that can be fault-tolerantly implemented, for example, Clifford+$T$ gates. Here, $T$ gate is usually regarded as an essential resource for quantum computation because its action cannot be simulated efficiently on classical computers and it is experimentally difficult to implement fault-tolerantly. Practically, it is highly likely that only a limited number of $T$ gates are available in the near future. Pre-FTQC era, due to the constraint on available resources, it is vital to precisely estimate the decomposition error of a whole circuit. In this paper, we propose that the Clifford+$T$ decomposition error for a given quantum circuit containing a large number of quantum gates can be modeled as the depolarizing noise by averaging the decomposition error for each quantum gate in the circuit, and our model provides more accurate error estimation than the naive estimation. We exemplify this by taking unitary coupled-cluster (UCC) ansatz used in the applications of quantum computers to quantum chemistry as an example. We theoretically evaluate the approximation error of UCC ansatz when decomposed into Clifford+$T$ gates, and the numerical simulation for a wide variety of molecules verified that our model well explains the total decomposition error of the ansatz. Our results enable the precise and efficient usage of quantum resources in the early-stage applications of quantum computers and fuel further research towards what quantum computation can achieve in the upcoming future.

  
  
• Quick design of feasible tensor networks for constrained combinatorial optimization
  

  Quantum 9, 1799 (2025).

  https://doi.org/10.22331/q-2025-07-21-1799

  Quantum computers are expected to enable fast solving of large-scale combinatorial optimization problems. However, their limitations in fidelity and the number of qubits prevent them from handling real-world problems. Recently, a quantum-inspired solver using tensor networks has been proposed, which works on classical computers. Particularly, tensor networks have been applied to constrained combinatorial optimization problems for practical applications. By preparing a specific tensor network to sample states that satisfy constraints, feasible solutions can be searched for without the method of penalty functions. Previous studies have been based on profound physics, such as U(1) gauge schemes and high-dimensional lattice models. In this study, we devise to design feasible tensor networks using elementary mathematics without such a specific knowledge. One approach is to construct tensor networks with nilpotent-matrix manipulation. The second is to algebraically determine tensor parameters. We showed mathematically that such feasible tensor networks can be constructed to accommodate various types of constraints. For the principle verification, we numerically constructed a feasible tensor network for facility location problem, to find much faster construction than conventional methods. Then, by performing imaginary time evolution, feasible solutions were always obtained, ultimately leading to the optimal solution.

  
  
• Estimation of Quantum Fisher Information via Stein’s Identity in Variational Quantum Algorithms
  

  Quantum 9, 1798 (2025).

  https://doi.org/10.22331/q-2025-07-21-1798

  The Quantum Fisher Information Matrix (QFIM) plays a crucial role in quantum optimization algorithms such as Variational Quantum Imaginary Time Evolution and Quantum Natural Gradient Descent. However, computing the full QFIM incurs a quadratic computational cost of $O(d^2)$ with respect to the number of parameters $d$, limiting its scalability for high-dimensional quantum systems. To address this limitation, stochastic methods such as the Simultaneous Perturbation Stochastic Approximation (SPSA) have been employed to reduce computational complexity to a constant (Quantum 5, 567 (2021)). In this work, we propose an alternative estimation framework based on Stein's identity that also achieves constant computational complexity. Furthermore, our method reduces the quantum resources required for QFIM estimation compared to the SPSA approach. We provide numerical examples using the transverse-field Ising model and the lattice Schwinger model to demonstrate the feasibility of applying our method to realistic quantum systems.

  
  
• Entanglement and Stabilizer entropies of random bipartite pure quantum states
  

  Quantum 9, 1797 (2025).

  https://doi.org/10.22331/q-2025-07-21-1797

  The interplay between non-stabilizerness and entanglement in random states is a very rich arena of study for the understanding of quantum advantage and complexity. In this work, we tackle the problem of such interplay in random pure quantum states. We show that while there is a strong dependence between entanglement and magic, they are, surprisingly, perfectly uncorrelated. We compute the expectation value of non-stabilizerness given the Schmidt spectrum (and thus entanglement). At a first approximation, entanglement determines the average magic on the Schmidt orbit. However, there is a finer structure in the average magic distinguishing different orbits where the flatness of entanglement spectrum is involved.

  
  

Monday, July 14, 2025

• End-to-end switchless architecture for fault-tolerant photonic quantum computing
  

  Quantum 9, 1796 (2025).

  https://doi.org/10.22331/q-2025-07-14-1796

  Photonics represents one of the most promising approaches to large-scale quantum computation with millions of qubits and billions of gates, owing to the potential for room-temperature operation, high clock speeds, miniaturization of photonic circuits, and repeatable fabrication processes in commercial photonic foundries. We present an end-to-end architecture for fault-tolerant continuous variable (CV) quantum computation using only passive on-chip components that can produce photonic qubits above the fault tolerance threshold with probabilities above 90%, and encodes logical qubits using physical qubits sampled from a distribution around the fault tolerance threshold. By requiring only low photon number resolution, the architecture enables the use of high-bandwidth photodetectors in CV quantum computing. Simulations of our qubit generation and logical encoding processes show a Gaussian cluster squeezing threshold of 12 dB to 13 dB. Additionally, we present a novel magic state generation protocol which requires only 13 dB of cluster squeezing to produce magic states with an order of magnitude higher probability than existing approaches, opening up the path to universal fault-tolerant quantum computation at less than 13 dB of cluster squeezing.

  
  
• Transforming graph states via Bell state measurements
  

  Quantum 9, 1795 (2025).

  https://doi.org/10.22331/q-2025-07-14-1795

  Graph states are key resources for measurement-based quantum computing, which is particularly promising for photonic systems. Fusions are probabilistic Bell state measurements, measuring pairs of parity operators of two qubits. Fusions can be used to connect/entangle different graph states, making them a powerful resource for measurement-based and related fusion-based quantum computing. There are several different graph structures and types of Bell state measurements, yet the associated graph transformations have only been analyzed for specific cases. Here, we provide a full set of graph transformation rules and give an intuitive visualization based on Venn diagrams of local neighborhoods of graph nodes. We derive these graph transformations for all types of rotated type-II fusion, showing that there are five different fusion success cases. Finally, we give application examples of the derived graph transformation rules and show that they can be used to construct graph codes or simulate fusion networks.

  
  
• Field theory for monitored Brownian SYK clusters
  

  Quantum 9, 1794 (2025).

  https://doi.org/10.22331/q-2025-07-14-1794

  We consider the time evolution of multiple clusters of Brownian Sachdev-Ye-Kitaev (SYK), i.e. systems of N Majorana fermions with a noisy interaction term. In addition to the unitary evolution, we introduce two-fermion monitorings. We construct a coherent states path integral of the dynamics by generalizing spin coherent states for higher symmetry groups. We then demonstrate that the evolution of the replicated density matrix can be described by an effective field theory for the "light" degrees of freedom, i.e. the quantum fluctuations generated by the unitary evolution. This method is applied to both quadratic, where the field theory reduces to the nonlinear sigma model (NLSM), and also to interacting SYK clusters. We show that in the stationary regime, two monitored clusters exhibit linear-in-$N$ entanglement, with a proportionality factor dependent on the strength of the unitary coupling.

  
  

Friday, July 11, 2025

• Quantum Enhanced Sensitivity through Many-Body Bloch Oscillations
  

  Quantum 9, 1793 (2025).

  https://doi.org/10.22331/q-2025-07-11-1793

  We investigate the sensing capacity of non-equilibrium dynamics in quantum systems exhibiting Bloch oscillations. By focusing on the resource efficiency of the probe, quantified by quantum Fisher information, we find different scaling behaviors in two different phases, namely localized and extended. Our results provide a quantitative ansatz for quantum Fisher information in terms of time, probe size, and the number of excitations. In the long-time regime, the quantum Fisher information is a quadratic function of time, touching the Heisenberg limit. The system size scaling drastically depends on the phase changing from quantum-enhanced scaling in the extended phase to size-independent behavior in the localized phase. Furthermore, increasing the number of excitations always enhances the precision of the probe, although, in the interacting systems the enhancement becomes less eminent than the non-interacting probes. This is due to the induced localization by increasing the interaction between the excitations. We show that a simple particle configuration measurement together with a maximum likelihood estimation can closely reach the ultimate precision limit in both single- and multi-particle probes.

  
  
• Learning Feedback Mechanisms for Measurement-Based Variational Quantum State Preparation
  

  Quantum 9, 1792 (2025).

  https://doi.org/10.22331/q-2025-07-11-1792

  This work introduces a self-learning protocol that incorporates measurement and feedback into variational quantum circuits for efficient quantum state preparation. By combining projective measurements with conditional feedback, the protocol learns state preparation strategies that extend beyond unitary-only methods, leveraging measurement-based shortcuts to reduce circuit depth. Using the spin-1 Affleck-Kennedy-Lieb-Tasaki state as a benchmark, the protocol learns high-fidelity state preparation by overcoming a family of measurement induced local minima through adjustments of parameter update frequencies and ancilla regularization. Despite these efforts, optimization remains challenging due to the highly non-convex landscapes inherent to variational circuits. The approach is extended to larger systems using translationally invariant ansätze and recurrent neural networks for feedback, demonstrating scalability. Additionally, the successful preparation of a specific AKLT state with desired edge modes highlights the potential to discover new state preparation protocols where none currently exist. These results indicate that integrating measurement and feedback into variational quantum algorithms provides a promising framework for quantum state preparation.

  
  
• Quantum PCPs: on Adaptivity, Multiple Provers and Reductions to Local Hamiltonians
  

  Quantum 9, 1791 (2025).

  https://doi.org/10.22331/q-2025-07-11-1791

  We define a general formulation of quantum PCPs, which captures adaptivity and multiple unentangled provers, and give a detailed construction of the quantum reduction to a local Hamiltonian with a constant promise gap. The reduction turns out to be a versatile subroutine to prove properties of quantum PCPs, allowing us to show: (i) Non-adaptive quantum PCPs can simulate adaptive quantum PCPs when the number of proof queries is constant. In fact, this can even be shown to hold when the non-adaptive quantum PCP picks the proof indices simply uniformly at random from a subset of all possible index combinations, answering an open question by Aharonov, Arad, Landau and Vazirani (STOC '09). (ii) If the $q$-local Hamiltonian problem with constant promise gap can be solved in $\mathsf{QCMA}$, then $\mathsf{QPCP}[q] \subseteq \mathsf{QCMA}$ for any $q \in O(1)$. (iii) If $\mathsf{QMA}(k)$ has a quantum PCP for any $k \leq \text{poly}(n)$, then $\mathsf{QMA}(2) = \mathsf{QMA}$, connecting two of the longest-standing open problems in quantum complexity theory. Moreover, we also show that there exist (quantum) oracles relative to which certain quantum PCP statements are false. Hence, any attempt to prove the quantum PCP conjecture requires, just as was the case for the classical PCP theorem, (quantumly) non-relativizing techniques.

  
  
• Unstructured Adiabatic Quantum Optimization: Optimality with Limitations
  

  Quantum 9, 1790 (2025).

  https://doi.org/10.22331/q-2025-07-11-1790

  In the circuit model of quantum computing, amplitude amplification techniques can be used to find solutions to NP-hard problems defined on $n$-bits in time $\text{poly}(n) 2^{n/2}$. In this work, we investigate whether such general statements can be made for adiabatic quantum optimization, as provable results regarding its performance are mostly unknown. Although a lower bound of $\Omega(2^{n/2})$ has existed in such a setting for over a decade, a purely adiabatic algorithm with this running time has been absent. We show that adiabatic quantum optimization using an unstructured search approach results in a running time that matches this lower bound (up to a polylogarithmic factor) for a broad class of classical local spin Hamiltonians. For this, it is necessary to bound the spectral gap throughout the adiabatic evolution and compute beforehand the position of the avoided crossing with sufficient precision so as to adapt the adiabatic schedule accordingly. However, we show that the position of the avoided crossing is approximately given by a quantity that depends on the degeneracies and inverse gaps of the problem Hamiltonian and is NP-hard to compute even within a low additive precision. Furthermore, computing it exactly (or nearly exactly) is #P-hard. Our work indicates a possible limitation of adiabatic quantum optimization algorithms, leaving open the question of whether provable Grover-like speed-ups can be obtained for any optimization problem using this approach.

  
  

Wednesday, July 9, 2025

• Deep Circuit Compression for Quantum Dynamics via Tensor Networks
  

  Quantum 9, 1789 (2025).

  https://doi.org/10.22331/q-2025-07-09-1789

  Dynamic quantum simulation is a leading application for achieving quantum advantage. However, high circuit depths remain a limiting factor on near-term quantum hardware. We present a compilation algorithm based on Matrix Product Operators for generating compressed circuits enabling real-time simulation on digital quantum computers, that for a given depth are more accurate than all Trotterizations of the same depth. By the efficient use of environment tensors, the algorithm is scalable in depth far beyond prior work, and we present circuit compilations of up to 64 layers of $SU(4)$ gates. Surpassing only 1D circuits, our approach can flexibly target a particular quasi-2D gate topology. We demonstrate this by compiling a 52-qubit 2D Transverse-Field Ising propagator onto the IBM Heavy-Hex topology. For all circuit depths and widths tested, we produce circuits with smaller errors than all equivalent depth Trotter unitaries, corresponding to reductions in error by up to 4 orders of magnitude and circuit depth compressions with a factor of over 6.

  
  
• Classical Simulation of High Temperature Quantum Ising Models
  

  Quantum 9, 1788 (2025).

  https://doi.org/10.22331/q-2025-07-09-1788

  We consider generalized quantum Ising models, including those which could describe disordered materials or quantum annealers, and we prove that for all temperatures above a system-size independent threshold the path integral Monte Carlo method based on worldline heat-bath updates always mixes to stationarity in time $\mathcal{O}(n \log n)$ for an $n$ qubit system, and therefore provides a fully polynomial-time approximation scheme for the partition function. This result holds whenever the temperature is greater than four plus twice the maximum interaction degree (valence) over all qubits, measured in units of the local coupling strength. For example, this implies that the classical simulation of the thermal state of a superconducting device modeling a frustrated quantum Ising model with maximum valence of 6 and coupling strengths of 1 GHz is always possible at temperatures above 800 mK. Despite the quantum system being at high temperature, the classical spin system resulting from the quantum-to-classical mapping contains strong couplings which cause the single-site Glauber dynamics to mix slowly, therefore this result depends on the use of worldline updates (which are a form of cluster updates that can be implemented efficiently). This result places definite constraints on the temperatures required for a quantum advantage in analog quantum simulation with various NISQ devices based on equilibrium states of quantum Ising models.

  
  
• Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories?
  

  Quantum 9, 1787 (2025).

  https://doi.org/10.22331/q-2025-07-09-1787

  Quantum trajectories of a Markovian open quantum system arise from the back-action of measurements performed in the environment with which the system interacts. In this work, we consider counting measurements of quantum jumps, corresponding to different representations of the same quantum master equation. We derive necessary and sufficient conditions under which these different measurements give rise to the same unravelled quantum master equation, which governs the dynamics of the probability distribution over pure conditional states of the system. Since that equation uniquely determines the stochastic dynamics of a conditional state, we also obtain necessary and sufficient conditions under which different measurements result in identical quantum trajectories. We then consider the joint stochastic dynamics for the conditional state and the measurement record. We formulate this in terms of labelled quantum trajectories, and derive necessary and sufficient conditions under which different representations lead to equivalent labelled quantum trajectories, up to permutations of labels. As those conditions are generally stricter, we finish by constructing coarse-grained measurement records, such that equivalence of the corresponding partially-labelled trajectories is guaranteed by equivalence of the trajectories alone. These general results are illustrated by two examples that demonstrate permutation of labels, and equivalence of different quantum trajectories.