In briefExponential query advantage from Stinespring dilation unitary access in quantum channel learning
SummaryThis paper studies learning how close an unknown quantum channel is to a unitary channel, measured by the optimal average gate fidelity (OAGF). For constant Kraus rank and environment dimension polylog(d), an algorithm estimates OAGF using polylog(d) queries to the Stinespring dilation unitary and its inverse. Under black-box access, at least Ω(√d) queries are required, showing an exponential separation between the two access models.
Manaki Arihara, Satoshi Yoshida, Philip Taranto et al.
In briefQuantum state learning beyond approximate unitary designs
SummaryThe paper examines whether approximate unitary designs can replace exact designs in quantum state learning. It shows that even exponentially small design error need not preserve the learning guarantees of exact designs, so guarantees should be derived from the measurement circuit structure. For classical shadows, it proves that logarithmic-depth two-layer Clifford circuits give an unbiased observable estimator matching global Clifford variance scaling.
WhyProves log-depth two-layer Clifford circuits preserve global Clifford variance for classical shadows and characterizes limits of approximate designs, a novel, rigorous contribution useful within the s
In briefA method for predicting properties of Scrooge ensembles with fewer samples
SummaryThe paper studies Scrooge ensembles, the maximally random ensembles whose average density matrix equals a given ρ, which matter for quantum many-body dynamics and quantum information. It gives a polynomial approximation to the Scrooge k-th moments whose error threshold improves from inverse polynomial to exponential in 1/||ρ||∞. Based on this, it presents the first efficient quantum algorithm for estimating observable expectation values, using Õ(k³/ε⁵) copies of ρ.
WhyImproves the error threshold from inverse polynomial to exponential and gives the first efficient observable-estimation algorithm with solid analysis.
In briefLocalising logical information in stabiliser codes using single-qubit measurements
SummaryThis paper studies stabiliser path finding (SPF), a method for concentrating logical information from a stabiliser code with lost qubits onto a target qubit using one round of single-qubit measurements. It introduces g-SPF, which localises information onto at most g unspecified target qubits, and proves that for i.i.d. loss probability p<1/2 and large planar surface codes, this succeeds with probability tending to one, establishing a localisation threshold. The authors also present an exact integer linear programming algorithm and a faster heuristic decoding-based algorithm, validated on the surface code.
In briefQuantum query complexity of semigroup products
SummaryThis paper studies how many quantum queries are needed to compute a semigroup product x_1…x_n when each query reveals one input element and the multiplication table is known. The authors introduce a product breadth parameter β, which characterizes the complexity for finite commutative aperiodic monoids. For arbitrary finite aperiodic semigroups, they improve a previous upper bound, and show the dependence on semigroup size is nearly tight.
WhyCharacterizes quantum query complexity of commutative aperiodic monoids via product breadth and substantially improves the general semigroup upper bound with near-tight lower bounds.
In briefSingle-shot state preparation threshold: a rigorous theorem and statistical mechanical mapping
SummaryThis paper studies the threshold for preparing logical codewords using one round of noisy syndrome measurements, called single-shot state preparation. The authors prove that for CSS quantum LDPC codes with at least logarithmic distance, linear confinement alone guarantees a nonzero threshold, and under linear soundness the residual data error is local stochastic. They also develop a statistical mechanical mapping expressing the logical error rate as a partition function, and Monte Carlo simulations on the three-dimensional toric code suggest sublinear soundness can also support the threshold.
WhyProves linear confinement alone guarantees a single-shot preparation threshold, challenging the soundness-necessary belief, with a statistical-mechanical mapping and Monte Carlo support.
In briefA review of quantum algorithms for fluid dynamics simulation
SummaryThis paper reviews quantum methods for solving the partial differential equations used in computational fluid dynamics. It covers fully quantum approaches such as HHL, QSVT, and quantum lattice Boltzmann methods, along with hybrid approaches like quantum physics-informed neural networks. The authors also examine tensor-network representations and benchmark problems, concluding that any quantum advantage depends strongly on the specific problem.
Mario Guillaume Cecile, Nis-Luca van H\"ulst, Tomohiro Hashizume et al.
In briefProof that Haah's 3D cubic code thermalizes rapidly, settling whether it is a self-correcting quantum memory
SummaryHaah's 3D cubic code was proposed as a candidate for a self-correcting quantum memory in three dimensions, relying on the absence of string logical operators to suppress thermal errors. This paper rigorously shows that the code thermalizes rapidly at every positive temperature, answering a long-standing open question. The proof uses a framework that converts a decay-of-correlations condition into a modified logarithmic Sobolev inequality for the Davies generator.
WhyRigorously resolves a long-standing open question, proving rapid mixing at every positive temperature for Haah's cubic code via a modified log-Sobolev inequality.
Sebastian Stengele, Libor Caha, \'Angela Capel et al.
In briefConfocal imaging using biphoton correlations for pinhole-free, parallel optical sectioning
SummaryConfocal microscopy normally achieves optical sectioning through point-by-point scanning and physical pinholes, which limits imaging speed. This work shows that confocal sectioning can arise directly from quantum measurement, using spatial correlations in entangled biphoton states. Spatially resolved coincidence measurements in a widefield system suppress out-of-focus contributions, giving parallel sectioning across the field of view without pinholes or mechanical scanning. The axial response is √2 times narrower than that of classical confocal imaging, owing to position-momentum entanglement.
In briefScaling law of variational quantum algorithms: how these hybrid quantum-classical methods behave as problem size grows
SummaryThis paper studies how variational quantum algorithms scale using large numerical experiments on combinatorial optimization problems. The experiments reach up to 5000 qubits with circuit depth O(log n) and a classically simulable ansatz. The converged energies differ from the optimal or reference energies reported in benchmarks by no more than 0.5%.
In briefFast, reliable quantum process tomography via a closed-form projection that extends quantum state tomography methods to channel estimation
SummaryThis paper studies quantum process tomography (QPT), which estimates quantum channels from measurements, typically by lifting quantum state tomography (QST) methods through the Choi isomorphism while enforcing trace preservation. The authors show that the widely used partial normalization is the exact fidelity projection onto Choi states of quantum channels. As a result, any QST algorithm with fidelity guarantees yields a QPT algorithm with the same sample complexity via a closed-form congruence. The non-adaptive Fidelity Projected Least Squares protocol recovers the Choi rank and reaches infidelity ε using channel uses proportional to 1/ε. Numerical results show improved accuracy over projected least squares for low-Choi-rank channels, with orders-of-magnitude gains in the time and memory of the trace-preservation step and the estimate.
WhyShows partial normalization is the exact fidelity projection onto Choi states, transferring QST guarantees to QPT with sample-complexity bounds and numerical validation.
In briefFew Measurements, Many Constraints: Correlation-Enhanced Learning of Quantum Systems
SummaryThe paper shows that correlations among quantum observables can reduce the complexity of quantum learning, as a polynomial number of chosen measurements can bound exponentially many dependent unmeasured quantities. Based on this, the authors design correlation-informed algorithms that estimate entanglement and magic in 100-qubit systems, reporting lower relative error than shadow tomography and neural-state methods. The protocols need no entangling gates before measurement and are said to be testable on current quantum computers.
In briefFault-tolerant cost of shallow QAOA on near-symmetric optimization problems
SummaryThe paper studies the fault-tolerant cost of depth-one QAOA, which Montanaro and Zhou showed can find planted solutions to certain near-symmetric constraint satisfaction problems. The authors show that small-angle Clifford+T rotation synthesis reduces the non-Clifford cost per circuit to about n² for any clause locality. Compiling the circuit requires the explicit clause list, and degree-one Fourier coefficients can leak information about the planted solution. The authors also construct problem families where quadratic non-Clifford scaling and hard exact optimization coexist.
Jernej Rudi Fin\v{z}gar, Martin Leib, Elisabeth Wybo
In briefDistilling N-qubit stabilizer states on a star network
SummaryThis paper presents an entanglement distillation protocol that uses an arbitrary [[n,k,d]] stabilizer code to turn noisy N-qubit GHZ states into k logical copies. It works on a star network with local operations and scales efficiently to any N. Numerical tests with the 5-qubit, toric, and [[144,12,12]] codes under depolarizing noise show higher final GHZ fidelity than sending bare GHZ states at rates up to about 6%. The authors also prove the protocol applies to any N-qubit CSS stabilizer state.
Theodore M. Mahaffey, Chaohan Cui, Saikat Guha et al.
In briefQuantum sensing and learning of Hamiltonians whose parameters change randomly over time
SummaryThe paper introduces stochastically evolving Hamiltonians (SEHs), local Hamiltonians whose coefficients follow stochastic differential equations, and studies their theoretical properties. It considers Hamiltonian learning for SEHs by reanalysing and extending the Huang-Tong-Fang-Su protocol, which first achieved the Heisenberg limit for coefficient learning. The authors delineate theoretically when the Heisenberg limit can and cannot be retained, and develop quantum sensing and Hamiltonian simulation tools that may apply to similar settings.
