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Quantum is an open-access peer-reviewed journal for quantum science and related fields. Quantum is non-profit and community-run: an effort by […] [bridged from https://quantum-journal.org/ on the web: https://fed.brid.gy/web/quantum-journal.org ]

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Latest posts by Quantum @quantum-journal.org.web.brid.gy

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Near-optimal coherent state discrimination via continuously labelled non-Gaussian measurements Quantum 10, 2016 (2026). https://doi.org/10.22331/q-2026-03-09-2016 Quantum state discrimination plays a central role in quantum information and communication. For the discrimination of optical quantum states, the two most widely adopted measurement techniques are photon detection, which produces discrete outcomes, and homodyne detection, which produces continuous outcomes. While various protocols using photon detection have been proposed for optimal and near-optimal discrimination between two coherent states, homodyne detection is known to have higher error rates, with its minimum achievable error rate often referred to as the Gaussian limit. In this work, we demonstrate that, despite the fundamental differences between discretely labelled and continuously labelled measurements, continuously labelled non-Gaussian measurements can also achieve near-optimal coherent state discrimination. We design two discrimination protocols that surpass the Gaussian limit: one using non-Gaussian unitary operations with homodyne detection, and another based on orthogonal polynomials. Our results show that photon detection is not required for near-optimal coherent state discrimination and that we can achieve error rates close to the Helstrom bound at low energies with continuously labelled measurements. We also find that our schemes maintain an advantage over the photon detection-based Kennedy receiver for a moderate range of coherent state amplitudes.
09.03.2026 11:37 👍 0 🔁 0 💬 0 📌 0
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Efficient Computation of Generalized Noncontextual Polytopes and Quantum violation of their Facet Inequalities Quantum 10, 2015 (2026). https://doi.org/10.22331/q-2026-03-09-2015 Finding a set of empirical criteria fulfilled by any theory satisfying the generalized notion of noncontextuality is a challenging task of both operational and foundational importance. This work presents a methodology for constructing the noncontextual polytope while ensuring that the dimension of the polytope associated with the preparations remains constant regardless of the number of measurements and their outcome size. The facet inequalities of the noncontextual polytope can thus be obtained in a computationally efficient manner. We illustrate the efficacy of our methodology through several distinct contextuality scenarios. Our investigation uncovers several hitherto unexplored noncontextuality inequalities and demonstrates applications of quantum contextual correlations in certification of non-projective measurements, witnessing the dimension of quantum systems, and randomness certification.
09.03.2026 11:28 👍 0 🔁 0 💬 0 📌 0
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Utility-Scale Quantum State Preparation: Classical Training using Pauli Path Simulation Quantum 10, 2014 (2026). https://doi.org/10.22331/q-2026-03-09-2014 We use Pauli Path simulation to variationally obtain parametrized circuits for preparing ground states of various quantum many-body Hamiltonians. These include the quantum Ising model in one dimension, in two dimensions on square and heavy-hex lattices, and the Kitaev honeycomb model, all at system sizes of one hundred qubits or more – sizes at which generic quantum circuits are beyond the reach of exact state-vector simulation – thereby reaching utility scale. We benchmark the Pauli Path simulation results against exact ground-state energies when available, and against density-matrix renormalization group calculations otherwise, finding strong agreement. To further assess the quality of the variational states, we evaluate the magnetization in the x and z directions for the quantum Ising models and compute the topological entanglement entropy for the Kitaev honeycomb model. Finally, we prepare approximate ground states of the Kitaev honeycomb model with 48 qubits, in both the gapped and gapless regimes, on Quantinuum's System Model H2 quantum computer using parametrized circuits obtained from Pauli Path simulation. We achieve a relative energy error of approximately $5\%$ without error mitigation and demonstrate the braiding of Abelian anyons on the quantum device beyond fixed-point models.
09.03.2026 09:41 👍 0 🔁 0 💬 0 📌 0
Quantum Supermaps are Characterized by Locality Quantum 10, 2013 (2026). https://doi.org/10.22331/q-2026-03-09-2013 We provide a new characterisation of quantum supermaps in terms of an axiom that refers only to sequential and parallel composition. Consequently, we generalize quantum supermaps to arbitrary monoidal categories and operational probabilistic theories. We do so by providing a simple definition of $\textit{locally-applicable transformation}$ on a monoidal category. The definition can be rephrased in the language of category theory using the principle of naturality, and can be given an intuitive diagrammatic representation in terms of which all proofs are presented. In our main technical contribution, we use this diagrammatic representation to show that locally-applicable transformations on quantum channels are in one-to-one correspondence with deterministic quantum supermaps. This alternative characterization of quantum supermaps is proven to work for more general multiple-input supermaps such as the quantum switch and on arbitrary normal convex spaces of quantum channels such as those defined by satisfaction of signaling constraints.
09.03.2026 09:31 👍 0 🔁 0 💬 0 📌 0
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Bridging Classical and Quantum Information Scrambling with the Operator Entanglement Spectrum Quantum 10, 2012 (2026). https://doi.org/10.22331/q-2026-03-05-2012 Universal features of chaotic quantum dynamics underlie our understanding of thermalization in closed quantum systems and the complexity of quantum computations. Reversible automaton circuits, comprised of classical logic gates, have emerged as a tractable means to study such dynamics. Despite generating no entanglement in the computational basis, these circuits nevertheless capture many features expected from fully quantum evolutions. In this work, we demonstrate that the differences between automaton dynamics and fully quantum dynamics are revealed by the operator entanglement spectrum, much like the entanglement spectrum of a quantum state distinguishes between the dynamics of states under Clifford and Haar random circuits. While the operator entanglement spectrum under random unitary dynamics is governed by the eigenvalue statistics of random Gaussian matrices, we show evidence that under random automaton dynamics it is described by the statistics of Bernoulli random matrices, whose entries are random variables taking values $0$ or $1$. We study the crossover between automaton and generic unitary operator dynamics as the automaton circuit is doped with gates that introduce superpositions, namely Hadamard or $R_x = e^{-i\frac{\pi}{4}X}$ gates. We find that a constant number of superposition-generating gates is sufficient to drive the operator dynamics to the random-circuit universality class, similar to earlier results on Clifford circuits doped with $T$ gates. This establishes the operator entanglement spectrum as a useful tool for probing the chaoticity and universality class of quantum dynamics.
05.03.2026 10:42 👍 0 🔁 0 💬 0 📌 0
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Universal and Efficient Quantum State Verification via Schmidt Decomposition and Mutually Unbiased Bases Quantum 10, 2011 (2026). https://doi.org/10.22331/q-2026-03-04-2011 Efficient verification of multipartite quantum states is crucial to many applications in quantum information processing. By virtue of Schmidt decomposition and mutually unbiased bases, here we propose a universal protocol to verify arbitrary multipartite pure quantum states using adaptive local projective measurements. Moreover, we establish a universal upper bound on the sample complexity that is independent of the local dimensions. Numerical calculations further indicate that Haar-random pure states can be verified with a constant sample cost, irrespective of the qudit number and local dimensions, even in the adversarial scenario in which the source cannot be trusted. As alternatives, we provide several simpler variants that can achieve similar high efficiencies without using Schmidt decomposition. The simplest variant consists of only two distinct tests.
04.03.2026 10:00 👍 0 🔁 0 💬 0 📌 0
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Self-restricting Noise and Exponential Relative Entropy Decay Under Unital Quantum Markov Semigroups Quantum 10, 2010 (2026). https://doi.org/10.22331/q-2026-03-04-2010 States of open quantum systems often decay continuously under environmental interactions. Quantum Markov semigroups model such processes in dissipative environments. It is known that finite-dimensional quantum Markov semigroups with GNS detailed balance universally obey complete modified logarithmic Sobolev inequalities (CMLSIs), yielding exponential decay of relative entropy to a subspace of fixed point states. We analyze continuous processes that combine dissipative with Hamiltonian time-evolution, precluding this notion of detailed balance. First, we find counterexamples to CMLSI-like decay for these processes and determine conditions under which it fails. In contrast, we prove that despite its absence at early times, exponential decay re-appears for unital, finite-dimensional quantum Markov semigroups at finite timescales. Finally, we show that when dissipation is much stronger than Hamiltonian time-evolution, the rate of eventual, exponential decay toward the semigroup's decoherence-free subspace is bounded inversely in the decay rate of the dissipative part alone. Dubbed self-restricting noise, this inverse relationship arises when strong damping suppresses effects that would otherwise spread noise beyond its initial subspace.
04.03.2026 09:20 👍 0 🔁 0 💬 0 📌 0
Coprime Bivariate Bicycle Codes and Their Layouts on Cold Atoms Quantum 10, 2009 (2026). https://doi.org/10.22331/q-2026-02-23-2009 Quantum computing is deemed to require error correction at scale to mitigate physical noise by reducing it to lower noise levels while operating on encoded logical qubits. Popular quantum error correction schemes include CSS code, of which surface codes provide regular mappings onto 2D planes suitable for contemporary quantum devices together with known transversal logical gates. Recently, qLDPC codes have been proposed as a means to provide denser encoding with the class of bivariate bicycle (BB) codes promising feasible design for devices. This work contributes a novel subclass of BB codes suitable for quantum error correction. This subclass employs $coprimes$ and the product $xy$ of the two generating variables $x$ and $y$ to construct polynomials, rather than using $x$ and $y$ separately as in vanilla BB codes. In contrast to vanilla BB codes, where parameters remain unknown prior to code discovery, the rate of the proposed code can be determined beforehand by specifying a factor polynomial as an input to the numerical search algorithm. Using this coprime-BB construction, we found a number of surprisingly short to medium-length codes that were previously unknown. We also propose a layout on cold atom arrays tailored for coprime-BB codes. The proposed layout reduces both move time for short to medium-length codes and the number of moves of atoms to perform syndrome extractions. We consider an error model with global laser noise on cold atoms, and simulations show that our proposed layout achieves significant improvements over prior work across the simulated codes.
23.02.2026 13:35 👍 0 🔁 0 💬 0 📌 0
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Generalized group designs: constructing novel unitary 2-, 3- and 4-designs Quantum 10, 2008 (2026). https://doi.org/10.22331/q-2026-02-23-2008 Unitary designs are essential tools in several quantum information protocols. Similarly to other design concepts, unitary designs are mainly used to facilitate averaging over a relevant space, in this case, the unitary group $\mathrm{U}(d)$. While it is known that exact unitary $t$-designs exist for any degree $t$ and dimension $d$, the most appealing type of designs, group designs (in which the elements of the design form a group), can provide at most $3$-designs. Moreover, even group $2$-designs can exist only in limited dimensions. In this paper, we present novel construction methods for creating exact generalized group designs based on the representation theory of the unitary group and its finite subgroups that overcome the $4$-design-barrier of unitary group designs. Furthermore, a construction is presented for creating generalized group $2$-designs in arbitrary dimensions. ##### Presentation _Generalised group designs overcoming the 3 design barrier and constructing novel 2_ At QIP2024
23.02.2026 13:14 👍 0 🔁 0 💬 0 📌 0
Localizing multipartite entanglement with local and global measurements Quantum 10, 2007 (2026). https://doi.org/10.22331/q-2026-02-23-2007 We study the task of localizing multipartite entanglement in pure quantum states onto a subsystem by measuring the remaining systems. To this end, we fix a multipartite entanglement measure and consider two quantities: the multipartite entanglement of assistance (MEA), defined as the entanglement measure averaged over the post-measurement states and maximized over arbitrary measurements; and the localizable multipartite entanglement (LME), defined in the same way but restricted to only local single-system measurements. Both quantities generalize previously considered bipartite entanglement localization measures. In our work we choose the n-tangle, the genuine multipartite entanglement concurrence and the concentratable entanglement (CE) as the underlying seed measure, and discuss the resulting MEA and LME quantities. First, we prove easily computable upper and lower bounds on MEA and LME and establish Lipschitz-continuity for the n-tangle and CE-based LME and MEA. Using these bounds we investigate the typical behavior of entanglement localization by deriving concentration inequalities for the MEA evaluated on Haar-random states and performing numerical studies for small tractable system sizes. We then turn our attention to protocols that transform graph states. We give a simple criterion based on a matrix equation to decided whether states with a specified n-tangle value can be obtained from a given graph state, providing no-go theorems for a broad class of such graph state transformations beyond the usual “local Clifford plus local Pauli measurement” framework. This analysis is generalized to weighted graph states, which provide a realistic error model in current experiments preparing graph state. Our entanglement localization framework certifies the near-optimality of recently discussed local-measurement protocols to transform uniformly weighted line graph states into GHZ states, even when considering arbitrary entangled measurements. Finally, we demonstrate how our MEA and LME quantities can be used to detect critical phenomena such as phase transitions in transversal field Ising models. Since entanglement localization is operationally relevant throughout quantum networking and measurement-based quantum computation, our framework of results based on the MEA and LME has the potential for broad applications in these fields.
23.02.2026 12:57 👍 0 🔁 0 💬 0 📌 0
Increasing the distance of topological codes with time vortex defects Quantum 10, 2006 (2026). https://doi.org/10.22331/q-2026-02-23-2006 We propose modifying topological quantum error correcting codes by incorporating space-time defects, termed “time vortices,'' to reduce the number of physical qubits required to achieve a desired logical error rate. A time vortex is inserted by adding a spatially varying delay to the periodic measurement sequence defining the code such that the delay accumulated on a homologically non-trivial cycle is an integer multiple of the period. We analyze this construction within the framework of the Floquet color code and optimize the embedding of the code on a torus along with the choice of the number of time vortices inserted in each direction. Asymptotically, the vortexed code requires less than half the number of qubits as the vortex-free code to reach a given code distance. We benchmark the performance of the vortexed Floquet color code by Monte Carlo simulations with a circuit-level noise model and demonstrate that the smallest vortexed code (with $30$ qubits) outperforms the vortex-free code with $42$ qubits.
23.02.2026 12:35 👍 0 🔁 0 💬 0 📌 0
Ideal stochastic process modeling with post-quantum quasiprobabilistic theories Quantum 10, 2005 (2026). https://doi.org/10.22331/q-2026-02-23-2005 In stochastic modeling, the excess entropy – the mutual information shared between a process's past and future – represents the fundamental lower bound of the memory needed to simulate its dynamics. However, this bound cannot be saturated by either classical machines or their enhanced quantum counterparts. Simulating a process fundamentally requires us to store more information in the present than is shared between the past and the future. Here, we consider a generalization of hidden Markov models beyond classical and quantum models, referred to as n-machines, that allow for negative quasiprobabilities. We show that under the collision entropy measure of information, the minimal memory of such models can equal the excess entropy. Our results suggest that negativity can be a useful resource for achieving nonclassical memory advantage.
23.02.2026 12:00 👍 0 🔁 0 💬 0 📌 0
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Complexity of geometrically local stoquastic Hamiltonians Quantum 10, 2004 (2026). https://doi.org/10.22331/q-2026-02-11-2004 The QMA-completeness of the local Hamiltonian problem is a landmark result of the field of Hamiltonian complexity that studies the computational complexity of problems in quantum many-body physics. Since its proposal, substantial effort has been invested in better understanding the problem for physically motivated important families of Hamiltonians. In particular, the QMA-completeness of approximating the ground state energy of local Hamiltonians has been extended to the case where the Hamiltonians are geometrically local in one and two spatial dimensions. Among those physically motivated Hamiltonians, stoquastic Hamiltonians play a particularly crucial role, as they constitute the manifestly sign-free Hamiltonians in Monte Carlo approaches. Interestingly, for such Hamiltonians, the problem at hand becomes more ''classical'', being hard for the class MA (the randomized version of NP) and its complexity has tight connections with derandomization. In this work, we prove that both the two- and one-dimensional geometrically local analogues remain MA-hard with high enough qudit dimension. Moreover, we show that related problems are StoqMA-complete.
11.02.2026 10:38 👍 0 🔁 0 💬 0 📌 0
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Theory of quantum error mitigation for non-Clifford gates Quantum 10, 2003 (2026). https://doi.org/10.22331/q-2026-02-10-2003 Quantum error mitigation techniques mimic noiseless quantum circuits by running several related noisy circuits and combining their outputs in particular ways. How well such techniques work is thought to depend strongly on how noisy the underlying gates are. Weakly-entangling gates, like $R_{ZZ}(\theta)$ for small angles $\theta$, can be much less noisy than entangling Clifford gates, like CNOT and CZ, and they arise naturally in circuits used to simulate quantum dynamics. However, such weakly-entangling gates are non-Clifford, and are therefore incompatible with two of the most prominent error mitigation techniques to date: probabilistic error cancellation (PEC) and the related form of zero-noise extrapolation (ZNE). This paper generalizes these techniques to non-Clifford gates, and comprises two complementary parts. The first part shows how to effectively transform any given quantum channel into (almost) any desired channel, at the cost of a sampling overhead, by adding random Pauli gates and processing the measurement outcomes. This enables us to cancel or properly amplify noise in non-Clifford gates, provided we can first characterize such gates in detail. The second part therefore introduces techniques to do so for noisy $R_{ZZ}(\theta)$ gates. These techniques are robust to state preparation and measurement (SPAM) errors, and exhibit concentration and sensitivity—crucial statistical properties for many experiments. They are related to randomized benchmarking, and may also be of interest beyond the context of error mitigation. We find that while non-Clifford gates can be less noisy than related Cliffords, their noise is fundamentally more complex, which can lead to surprising and sometimes unwanted effects in error mitigation. Whether this trade-off can be broadly advantageous remains to be seen.
10.02.2026 10:08 👍 0 🔁 0 💬 0 📌 0
On Certified Randomness from Fourier Sampling or Random Circuit Sampling Quantum 10, 2002 (2026). https://doi.org/10.22331/q-2026-02-10-2002 Certified randomness has a long history in quantum information, with many potential applications. Recently Aaronson and Hung proposed a novel public certified randomness protocol based on existing random circuit sampling (RCS) experiments. The security of their protocol, however, relies on non-standard complexity-theoretic conjectures which were not previously studied in the literature. Inspired by this work, we study certified randomness in the quantum random oracle model (QROM). We show that quantum Fourier Sampling can be used to define a publicly verifiable certified randomness protocol with black-box security without any computational assumptions. In addition to giving a certified randomness protocol in the QROM, our work can also be seen as supporting Aaronson and Hung's conjectures for RCS-based randomness generation, as our protocol is in some sense the "black-box version" of Aaronson and Hung's protocol. In further support of Aaronson and Hung's proposal, we prove a Fourier Sampling version of Aaronson and Hung's conjecture by extending Raz and Tal's separation of BQP vs PH. Our work complements the subsequent certified randomness protocol of Yamakawa and Zhandry (2022) in the QROM. Whereas the security of that protocol relied on the Aaronson-Ambainis conjecture, ours does not rely on any computational assumption – at the expense of requiring exponential-time classical verification. Our protocol also has a simple heuristic implementation.
10.02.2026 09:58 👍 0 🔁 0 💬 0 📌 0
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Minimising the number of edges in LC-equivalent graph states Quantum 10, 2001 (2026). https://doi.org/10.22331/q-2026-02-09-2001 Graph states are a powerful class of entangled states with numerous applications in quantum communication and quantum computation. Local Clifford (LC) operations that map one graph state to another can alter the structure of the corresponding graphs, including changing the number of edges. Here, we tackle the associated edge-minimisation problem: finding graphs with the minimum number of edges in the LC-equivalence class of a given graph. Such graphs are called minimum edge representatives (MER) and are crucial for minimising the resources required to create a graph state. We leverage Bouchet's algebraic formulation of LC-equivalence to encode the edge-minimisation problem as an integer linear program (EDM-ILP). We further propose a simulated annealing (EDM-SA) approach guided by the local clustering coefficient for edge minimisation. We identify new MERs for graph states with up to 16 qubits by combining EDM-SA and EDM-ILP. We extend the ILP to weighted-edge minimisation, where each edge has an associated weight, and prove that this problem is NP-complete. Finally, we employ our tools to minimise the resources required to create all-photonic generalised repeater graph states using fusion operations.
09.02.2026 11:42 👍 0 🔁 0 💬 0 📌 0
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Bosonic quantum Fourier codes Quantum 10, 2000 (2026). https://doi.org/10.22331/q-2026-02-09-2000 While 2-level systems, aka qubits, are a natural choice to perform a logical quantum computation, the situation is less clear at the physical level. Encoding information in higher-dimensional physical systems can indeed provide a first level of redundancy and error correction that simplifies the overall fault-tolerant architecture. A challenge then is to ensure universal control over the encoded qubits. Here, we explore an approach where information is encoded in an irreducible representation of a finite subgroup of $U(2)$ through an inverse quantum Fourier transform. We illustrate this idea by applying it to the real Pauli group $\langle X, Z\rangle$ in the bosonic setting. The resulting two-mode Fourier cat code displays good error correction properties and admits an experimentally-friendly universal gate set that we discuss in detail.
09.02.2026 11:34 👍 0 🔁 0 💬 0 📌 0
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Trotter error and gate complexity of the SYK and sparse SYK models Quantum 10, 1999 (2026). https://doi.org/10.22331/q-2026-02-09-1999 The Sachdev–Ye–Kitaev (SYK) model is a prominent model of strongly interacting fermions that serves as a toy model of quantum gravity and black hole physics. In this work, we study the Trotter error and gate complexity of the quantum simulation of the SYK model using Lie–Trotter–Suzuki formulas. Building on recent results by Chen and Brandão [6] — in particular their uniform smoothing technique for random matrix polynomials — we derive bounds on the first- and higher-order Trotter error of the SYK model, and subsequently find near-optimal gate complexities for simulating these models using Lie–Trotter–Suzuki formulas. For the $k$-local SYK model on $n$ Majorana fermions, at time $t$, our gate complexity estimates for the first-order Lie–Trotter–Suzuki formula scales with $\tilde{\mathcal{O}}(n^{k+\frac{5}{2}}t^2)$ for even $k$ and $\tilde{\mathcal{O}}(n^{k+3}t^2)$ for odd $k$, and the gate complexity of simulations using higher-order formulas scales with $\tilde{\mathcal{O}}(n^{k+\frac{1}{2}}t)$ for even $k$ and $\tilde{\mathcal{O}}(n^{k+1}t)$ for odd $k$. Given that the SYK model has $\Theta(n^k)$ terms, these estimates are close to optimal. These gate complexities can be further improved upon in the context of simulating the time evolution of an arbitrary fixed input state $|\psi\rangle$, leading to a $\mathcal{O}(n^2)$-reduction in gate complexity for first-order formulas and $\mathcal{O}(\sqrt{n})$-reduction for higher-order formulas. We also apply our techniques to the sparse SYK model, which is a simplified variant of the SYK model obtained by deleting all but a $\Theta(n)$ fraction of the terms in a uniformly i.i.d. manner. We find the average (over the random term removal) gate complexity for simulating this model using higher-order formulas scales with $\tilde{\mathcal{O}}(n^{1+\frac{1}{2}} t)$ for even $k$ and $\tilde{\mathcal{O}}(n^{2} t)$ for odd $k$. Similar to the full SYK model, we obtain a $\mathcal{O}(\sqrt{n})$-reduction simulating the time evolution of an arbitrary fixed input state $|\psi\rangle$. Our results highlight the potential of Lie–Trotter–Suzuki formulas for efficiently simulating the SYK and sparse SYK models, and our analytical methods can be naturally extended to other Gaussian random Hamiltonians.
09.02.2026 09:01 👍 0 🔁 0 💬 0 📌 0
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Variational quantum algorithms for permutation-based combinatorial problems: Optimal ansatz generation with applications to quadratic assignment problems and beyond Quantum 10, 1998 (2026). https://doi.org/10.22331/q-2026-02-09-1998 We present a quantum variational algorithm based on a novel circuit that generates all permutations that can be spanned by one- and two-qubits permutation gates. The construction of the circuits follows from group-theoretical results, most importantly the Bruhat decomposition of the group generated by the cx gates. These circuits require a number of qubits that scale logarithmically with the permutation dimension, and are therefore employable in near-term applications. We further augment the circuits with ancilla qubits to enlarge their span, and with these we build ansatze to tackle permutation-based optimization problems such as quadratic assignment problems, and graph isomorphisms. The resulting quantum algorithm, QuPer, is competitive with respect to classical heuristics and we could simulate its behavior up to a problem with 256 variables, requiring 20 qubits.
09.02.2026 08:37 👍 0 🔁 0 💬 0 📌 0
A 3D lattice defect and efficient computations in topological MBQC <p>Quantum 10, 1997 (2026).</p><a href="https://doi.org/10.22331/q-2026-02-06-1997">https://doi.org/10.22331/q-2026-02-06-1997</a><p class="abstract">We describe an efficient, fully fault-tolerant implementation of Measurement-Based Quantum Computation (MBQC) in the 3D cluster state. The two key novelties are (i) the introduction of a lattice defect in the underlying cluster state and (ii) the use of the Rudolph-Grover rebit encoding. Concretely, (i) allows for a topological implementation of the Hadamard gate, while (ii) does the same for the phase gate. Furthermore, we develop general ideas towards circuit compaction and algorithmic circuit verification, which we implement for the Reed-Muller code used for magic state distillation. Our performance analysis highlights the overall improvements provided by the new methods.</p><p class="further-content"></p>
06.02.2026 13:08 👍 0 🔁 0 💬 0 📌 0
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Quantum Circuit Optimization by Graph Coloring <p>Quantum 10, 1996 (2026).</p><a href="https://doi.org/10.22331/q-2026-02-06-1996">https://doi.org/10.22331/q-2026-02-06-1996</a><p class="abstract">This work shows that minimizing the depth of a quantum circuit composed of commuting operations reduces to a vertex coloring problem on an appropriately constructed graph, where gates correspond to vertices and edges encode non-parallelizability. The reduction leads to algorithms for circuit optimization by adopting any vertex coloring solver as an optimization backend. The approach is validated by numerical experiments as well as applications to known quantum circuits, including finite field multiplication and QFT-based addition.</p>
06.02.2026 13:03 👍 0 🔁 0 💬 0 📌 0
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Characterizing high-dimensional multipartite entanglement beyond Greenberger-Horne-Zeilinger fidelities <p>Quantum 10, 1995 (2026).</p><a href="https://doi.org/10.22331/q-2026-02-03-1995">https://doi.org/10.22331/q-2026-02-03-1995</a><p class="abstract">Characterizing entanglement of systems composed of multiple particles is a very complex problem that is attracting increasing attention across different disciplines related to quantum physics. The task becomes even more complex when the particles have many accessible levels, i.e., they are of high dimension, which leads to a potentially high-dimensional multipartite entangled state. These are important resources for an ever-increasing number of tasks, especially when a network of parties needs to share highly entangled states, e.g., for communicating more efficiently and securely. For these applications, as well as for purely theoretical arguments, it is important to be able to certify both the high-dimensional and the genuine multipartite nature of entangled states, possibly based on simple measurements. Here we derive a novel method that achieves this and improves over typical entanglement witnesses like the fidelity with respect to states of a Greenberger-Horne-Zeilinger (GHZ) form, without needing more complex measurements. We test our condition on paradigmatic classes of high-dimensional multipartite entangled states like imperfect GHZ states with random noise, as well as on purely randomly chosen ones and find that, in comparison with other available criteria our method provides a significant advantage and is often also simpler to evaluate.</p>
03.02.2026 12:47 👍 0 🔁 0 💬 0 📌 0
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Quantum Architecture Search with Unsupervised Representation Learning <p>Quantum 10, 1994 (2026).</p><a href="https://doi.org/10.22331/q-2026-02-03-1994">https://doi.org/10.22331/q-2026-02-03-1994</a><p class="abstract">Unsupervised representation learning presents new opportunities for advancing Quantum Architecture Search (QAS) on Noisy Intermediate-Scale Quantum (NISQ) devices. QAS is designed to optimize quantum circuits for Variational Quantum Algorithms (VQAs). Most QAS algorithms tightly couple the search space and search algorithm, typically requiring the evaluation of numerous quantum circuits, resulting in high computational costs and limiting scalability to larger quantum circuits. Predictor-based QAS algorithms mitigate this issue by estimating circuit performance based on structure or embedding. However, these methods often demand time-intensive labeling to optimize gate parameters across many circuits, which is crucial for training accurate predictors. Inspired by the classical neural architecture search algorithm $Arch2vec$, we investigate the potential of unsupervised representation learning for QAS without relying on predictors. Our framework decouples unsupervised architecture representation learning from the search process, enabling the learned representations to be applied across various downstream tasks. Additionally, it integrates an improved quantum circuit graph encoding scheme, addressing the limitations of existing representations and enhancing search efficiency. This predictor-free approach removes the need for large labeled datasets. During the search, we employ REINFORCE and Bayesian Optimization to explore the latent representation space and compare their performance against baseline methods. We further validate our approach by executing the best-discovered MaxCut circuits on IBM&#039;s ibm_sherbrooke quantum processor, confirming that the architectures retain optimal performance even under real hardware noise. Our results demonstrate that the framework efficiently identifies high-performing quantum circuits with fewer search iterations.</p>
03.02.2026 12:39 👍 0 🔁 0 💬 0 📌 0
Parameter estimation for quantum jump unraveling <p>Quantum 10, 1993 (2026).</p><a href="https://doi.org/10.22331/q-2026-02-02-1993">https://doi.org/10.22331/q-2026-02-02-1993</a><p class="abstract">We consider the estimation of parameters encoded in the measurement record of a continuously monitored quantum system in the jump unraveling, corresponding to a single-shot scenario, where information is continuously gathered. Here, it is generally difficult to assess the precision of the estimation procedure via the Fisher Information due to intricate temporal correlations and memory effects. In this paper we provide a full set of solutions to this problem. First, for multi-channel renewal processes we relate the Fisher Information to an underlying Markov chain and derive a easily computable expression for it. For non-renewal processes, we introduce a new algorithm that combines two methods: the monitoring operator method for metrology and the Gillespie algorithm which allows for efficient sampling of a stochastic form of the Fisher Information along individual quantum trajectories. We show that this stochastic Fisher Information satisfies useful properties related to estimation on a single run. Finally, we consider the case where some information is lost in data compression/post-selection and provide tools for computing the Fisher Information in this case. All scenarios are illustrated with instructive examples from quantum optics and condensed matter.</p>
02.02.2026 10:49 👍 0 🔁 0 💬 0 📌 0
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Scalable quantum simulator with an extended gate set in giant atoms <p>Quantum 10, 1992 (2026).</p><a href="https://doi.org/10.22331/q-2026-01-30-1992">https://doi.org/10.22331/q-2026-01-30-1992</a><p class="abstract">Quantum computation and quantum simulation require a versatile gate set to optimize circuit compilation for practical applications. However, existing platforms are often limited to specific gate types or rely on parametric couplers to extend their gate set, which compromises scalability. Here, we propose a scalable quantum simulator with an extended gate set based on giant-atom three-level systems, which can be implemented with superconducting circuits. Unlike conventional small atoms, giant atoms couple to the environment at multiple points, introducing interference effects that allow exceptional tunability of their interactions. By leveraging this tunability, our setup supports both CZ and iSWAP gates through simple frequency adjustments, eliminating the need for parametric couplers. This dual-gate capability enhances circuit efficiency, reducing the overhead for quantum simulation. As a demonstration, we showcase the simulation of spin dynamics in dissipative Heisenberg XXZ spin chains, highlighting the setup&#039;s ability to tackle complex open quantum many-body dynamics. Finally, we discuss how a two-dimensional extension of our system could enable fault-tolerant quantum computation, paving the way for a universal quantum processor.</p><p class="further-content"><h5>PresentatioN <span style="color: #cc99ff;"><a href="https://drive.google.com/file/d/1eEad-b7njX1veHJxbM07DXTOQTAnwAdP/view" style="color: #cc99ff;">Quantum simulation of open quantum many-body systems with giant atoms</a></span> by Guangze Chen and Anton Frisk Kockum</h5></p>
30.01.2026 10:12 👍 0 🔁 0 💬 0 📌 0
QMetro++ – Python optimization package for large scale quantum metrology with customized strategy structures <p>Quantum 10, 1991 (2026).</p><a href="https://doi.org/10.22331/q-2026-01-29-1991">https://doi.org/10.22331/q-2026-01-29-1991</a><p class="abstract">QMetro++ is a Python package that provides a set of tools for identifying optimal estimation protocols that maximize quantum Fisher information (QFI). Optimization can be performed for arbitrary configurations of input states, parameter-encoding channels, noise correlations, control operations, and measurements. The use of tensor networks and an iterative see-saw algorithm allows for an efficient optimization even in the regime of a large number of channel uses ($N\approx100$). Additionally, the package includes implementations of the recently developed methods for computing fundamental upper bounds on QFI, which serve as benchmarks for assessing the optimality of numerical optimization results. All functionalities are wrapped up in a user-friendly interface which enables the definition of strategies at various levels of detail.</p><p class="further-content"><h5 class="heading-element" dir="auto" tabindex="-1">QMetro++ – Python optimization package for large scale quantum metrology with customized strategy structures at <span style="color: #cc99ff;"><em><a href="https://github.com/pdulian/qmetro" style="color: #cc99ff;">Github</a></em></span></h5></p>
29.01.2026 12:50 👍 0 🔁 0 💬 0 📌 0
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Multi-qubit Rydberg gates between distant atoms <p>Quantum 10, 1990 (2026).</p><a href="https://doi.org/10.22331/q-2026-01-28-1990">https://doi.org/10.22331/q-2026-01-28-1990</a><p class="abstract">We propose an efficient protocol to realize multi-qubit gates in arrays of neutral atoms. The atoms encode qubits in the long-lived hyperfine sublevels of the ground electronic state. To realize the gate, we apply a global laser pulse to transfer the atoms to a Rydberg state with strong blockade interaction that suppresses simultaneous excitation of neighboring atoms arranged in a star-graph configuration. The number of Rydberg excitations, and thereby the parity of the resulting state, depends on the multiqubit input state. Upon changing the sign of the interaction and de-exciting the atoms with an identical laser pulse, the system acquires a geometric phase that depends only on the parity of the excited state, while the dynamical phase is completely canceled. Using single qubit rotations, this transformation can be converted to the C$_k$Z or C$_k$NOT quantum gate for $k+1$ atoms. We also present extensions of the scheme to implement quantum gates between distant atomic qubits connected by a quantum bus consisting of a chain of atoms.</p>
28.01.2026 10:31 👍 0 🔁 0 💬 0 📌 0
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NPA Hierarchy for Quantum Isomorphism and Homomorphism Indistinguishability <p>Quantum 10, 1989 (2026).</p><a href="https://doi.org/10.22331/q-2026-01-28-1989">https://doi.org/10.22331/q-2026-01-28-1989</a><p class="abstract">Mančinska and Roberson [FOCS&#039;20] showed that two graphs are quantum isomorphic if and only if they admit the same number of homomorphisms from any planar graph. Atserias et al. [JCTB&#039;19] proved that quantum isomorphism is undecidable in general, which motivates the study of its relaxations. In the classical setting, Roberson and Seppelt [ICALP&#039;23] characterized the feasibility of each level of the Lasserre hierarchy of semidefinite programming relaxations of graph isomorphism in terms of equality of homomorphism counts from an appropriate graph class. The NPA hierarchy, a noncommutative generalization of the Lasserre hierarchy, provides a sequence of semidefinite programming relaxations for quantum isomorphism. In the quantum setting, we show that the feasibility of each level of the NPA hierarchy for quantum isomorphism is equivalent to equality of homomorphism counts from an appropriate class of planar graphs. Combining this characterization with the convergence of the NPA hierarchy, and noting that the union of these classes is the set of all planar graphs, we obtain a new proof of the result of Mančinska and Roberson [FOCS&#039;20] that avoids the use of quantum groups. Moreover, this homomorphism indistinguishability characterization also yields a randomized polynomial-time algorithm deciding exact feasibility of each fixed level of the NPA hierarchy of SDP relaxations for quantum isomorphism.</p><p class="further-content"></p>
28.01.2026 10:22 👍 0 🔁 0 💬 0 📌 0
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Characterising memory in quantum channel discrimination via constrained separability problems <p>Quantum 10, 1988 (2026).</p><a href="https://doi.org/10.22331/q-2026-01-28-1988">https://doi.org/10.22331/q-2026-01-28-1988</a><p class="abstract">Quantum memories are a crucial precondition in many protocols for processing quantum information. A fundamental problem that illustrates this statement is given by the task of channel discrimination, in which an unknown channel drawn from a known random ensemble should be determined by applying it for a single time. In this paper, we characterise the quality of channel discrimination protocols when the quantum memory, quantified by the auxiliary dimension, is limited. This is achieved by formulating the problem in terms of separable quantum states with additional affine constraints that all of their factors in each separable decomposition obey. We discuss the computation of upper and lower bounds to the solutions of such problems which allow for new insights into the role of memory in channel discrimination. In addition to the single-copy scenario, this methodological insight allows to systematically characterise quantum and classical memories in adaptive channel discrimination protocols. Especially, our methods enabled us to identify channel discrimination scenarios where classical or quantum memory is required, and to identify the hierarchical and non-hierarchical relationships within adaptive channel discrimination protocols.</p>
28.01.2026 10:09 👍 0 🔁 0 💬 0 📌 0
A Computational Tsirelson’s Theorem for the Value of Compiled XOR Games <p>Quantum 10, 1987 (2026).</p><a href="https://doi.org/10.22331/q-2026-01-27-1987">https://doi.org/10.22331/q-2026-01-27-1987</a><p class="abstract">Nonlocal games are a foundational tool for understanding entanglement and constructing quantum protocols in settings with multiple spatially separated quantum devices. In this work, we continue the study initiated by Kalai et al. (STOC &#039;23) of compiled nonlocal games, played between a classical verifier and a single cryptographically limited quantum device. Our main result is that the compiler proposed by Kalai et al. is sound for any two-player XOR game. A celebrated theorem of Tsirelson shows that for XOR games, the quantum value is exactly given by a semidefinite program, and we obtain our result by showing that the SDP upper bound holds for the compiled game up to a negligible error arising from the compilation. This answers a question raised by Natarajan and Zhang (FOCS &#039;23), who showed soundness for the specific case of the CHSH game. Using our techniques, we obtain several additional results, including (1) tight bounds on the compiled value of parallel-repeated XOR games, (2) operator self-testing statements for any compiled XOR game, and (3) a “nice&#039;&#039; sum-of-squares certificate for any XOR game, from which operator rigidity is manifest.</p>
27.01.2026 14:57 👍 0 🔁 0 💬 0 📌 0