Quantum

Quantum 10, 2099 (2026). https://doi.org/10.22331/q-2026-05-08-2099 Current and near-term quantum hardware is constrained by limited qubit counts, circuit depth, and the high cost of repeated measurements. We address these challenges for solid-state Hamiltonians by introducing a logarithmic-qubit encoding that maps a system with $N$ physical sites onto only $\lceil \log_2 N \rceil$ qubits while m…

Quantum 10, 2098 (2026). https://doi.org/10.22331/q-2026-05-06-2098 In this paper, we develop the resource theory of quantum secret key. Operating under the assumption that entangled states with zero distillable key do not exist, we define the key cost of a quantum state, and device. We study its properties through the lens of a quantity that we call the key of formation. The main result of our p…

Quantum 10, 2097 (2026). https://doi.org/10.22331/q-2026-05-06-2097 We show the 2-Local Stoquastic Hamiltonian problem on a 2D square qubit lattice is StoqMA-complete. We achieve this by extending the spatially sparse circuit construction of Oliveira and Terhal, as well as the perturbative gadgets of Bravyi, DiVincenzo, Oliveira, and Terhal. Our main contributions demonstrate StoqMA circuits can …

Quantum 10, 2096 (2026). https://doi.org/10.22331/q-2026-05-06-2096 This paper aims to devise the shape of the external electromagnetic field that drives the spin dynamics of radical pairs to a quantum coherent state through maximization of the triplet-born singlet yield in biochemical reactions. The model is a Schrödinger system with spin Hamiltonians given by the sum of Zeeman interaction and h…

Quantum 10, 2095 (2026). https://doi.org/10.22331/q-2026-05-05-2095 State conversion is a fundamental task in quantum information processing. Quantum resource theories allow for analyzing and bounding conversions that use restricted sets of operations. In the context of continuous-variable systems, state conversions restricted to Gaussian operations are crucial for both fundamental and practical …

Quantum 10, 2094 (2026). https://doi.org/10.22331/q-2026-05-05-2094 Graph states are entangled states that are essential for quantum information processing. As experimental advances enable the realization of large-scale graph states, efficient fidelity estimation methods are crucial for assessing their robustness against noise. However, calculations of exact fidelity become intractable for large …

Quantum 10, 2093 (2026). https://doi.org/10.22331/q-2026-05-05-2093 Quantum circuit simulation is paramount to the verification and optimization of quantum algorithms, and considerable research efforts have been made towards efficient simulators. While circuits often contain high-level gates such as oracles and multi-controlled $X$ ($C^kX$) gates, existing simulation methods require compilation t…

Quantum 10, 2092 (2026). https://doi.org/10.22331/q-2026-05-05-2092 Calculating the quantum weight enumerator polynomial (WEP) is a valuable tool for characterizing quantum error-correcting (QEC) codes, but it is computationally hard for large or complex codes. The Quantum LEGO (QL) framework provides a tensor network approach for WEP calculation, in some cases offering superpolynomial speedups o…

Quantum 10, 2091 (2026). https://doi.org/10.22331/q-2026-05-05-2091 Quantum hypergraph states form a generalisation of the graph state formalism that goes beyond the pairwise (dyadic) interactions imposed by remaining inside the Gaussian approximation. Networks of such states are able to achieve universality for continuous variable measurement based quantum computation with only Gaussian measurem…

Quantum 10, 2090 (2026). https://doi.org/10.22331/q-2026-05-05-2090 We study higher order quantum maps in the context of a *-autonomous category of affine subspaces. We show that types of higher order maps can be identified with certain Boolean functions that we call type functions. By an extension of this identification, the algebraic structure of Boolean functions is inherited by some sets of q…

Quantum 10, 2089 (2026). https://doi.org/10.22331/q-2026-04-29-2089 We introduce regular language states, a family of quantum many-body states. They are built from a special class of formal languages, called regular, which has been thoroughly studied in the field of computer science. They can be understood as the superposition of all the words in a regular language and encompass physically releva…

Quantum 10, 2088 (2026). https://doi.org/10.22331/q-2026-04-28-2088 We prove new monogamy of entanglement bounds for two-local qudit Hamiltonians of rank-one projectors without one-local terms. In particular, we certify the maximum energy in terms of the maximum matching of the underlying interaction graph via low-degree sum-of-squares proofs. Algorithmically, we show that a simple matching-based…

Quantum 10, 2087 (2026). https://doi.org/10.22331/q-2026-04-28-2087 In unitary circuit games, two competing parties, an "entangler" and a "disentangler", can induce an entanglement phase transition in a quantum many-body system. The transition occurs at a certain rate at which the disentangler acts. We analyze such games within the context of matchgate dynamics, which equivalently corresponds to …

Quantum 10, 2086 (2026). https://doi.org/10.22331/q-2026-04-28-2086 We introduce $\texttt{RandomMeas.jl}$, a modular and high-performance open-source software package written in Julia for implementing and analyzing randomized measurement protocols in quantum computing. Randomized measurements provide a powerful framework for extracting properties of quantum states and processes such as expectatio…

Quantum 10, 2085 (2026). https://doi.org/10.22331/q-2026-04-28-2085 The coupling of a quantum system to an environment leads generally to decoherence, and it is detrimental to quantum correlations within the system itself. Yet some forms of quantum correlations can be robust to the presence of an environment – or may even be stabilized by it. Predicting (let alone understanding) them remains ardu…

Quantum 10, 2084 (2026). https://doi.org/10.22331/q-2026-04-28-2084 The question of “non-locality of a single photon'', which started with a paper by Tan, Walls and Collett (TWC, 1991) stirred a thirty years long debate. This hampered attempts to use the TWC interferometric scheme in quantum cryptography. The scheme involves a single photon 50-50 beam-split into two modes propagating to two spati…

Quantum 10, 2083 (2026). https://doi.org/10.22331/q-2026-04-24-2083 Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial connectivity. This raises the question of how to realize these codes with minimal overhead under physi…

Quantum 10, 2082 (2026). https://doi.org/10.22331/q-2026-04-23-2082 We present a formalism that allows for the direct manipulation and optimization of subspaces, circumventing the need to optimize individual states when using subspace methods. Using the determinant state mapping, we can naturally extend notions such as distance and energy to subspaces, as well as Monte Carlo estimators, recoverin…

Quantum 10, 2081 (2026). https://doi.org/10.22331/q-2026-04-23-2081 Waveguide quantum electrodynamics (QED) provides a powerful framework for engineering quantum interactions, traditionally relying on periodic photonic arrays with continuous energy bands. Here, we investigate waveguide QED in a fundamentally different environment: A one-dimensional photonic array whose hopping strengths are struc…

Quantum 10, 2080 (2026). https://doi.org/10.22331/q-2026-04-23-2080 Holonomic quantum computation exploits the geometric evolution of eigenspaces of a degenerate Hamiltonian to implement unitary evolution of computational states. In this work we introduce a framework for performing scalable quantum computation in atom experiments through a universal set of fully holonomic adiabatic gates. Through…