Selected papers | Quantum Research Center

Certifying the Rydberg-exposure limit of a globally driven controlled-Z gate

Sun, 08 Nov 2026 00:00:00 +0000

Neutral-atom CZ gates excite atoms to Rydberg states, and decay from those states is a leading source of gate error and atom loss, with loss probability about \Gamma T_R for average Rydberg time T_R. Can pulse shaping and longer gates make the exposure C=\Omega_{\max}T_R arbitrarily small when one global laser drives both atoms, with perfect blockade? Numerical optimal control had reached C\approx2.936, but no lower bound valid for all pulses existed. No: for every exact globally driven CZ gate in the perfect-blockade model, of any duration, 2.9312\le C_*<2.9359. The lower bound comes from a sum-of-squares certificate verified exactly over \mathbb Q(\sqrt2); the upper bound from an interval-arithmetic (Krawczyk) proof that an exact CZ pulse exists near a numerical candidate. The unrounded bounds differ by less than 0.16%.

Efficient Pauli truncation from operator stabilizer Rényi entropy

Sun, 08 Nov 2026 00:00:00 +0000

Classical simulation by Pauli propagation evolves an observable in the Heisenberg picture and keeps only its \chi largest Pauli coefficients. The operator stabilizer Rényi entropy (OSE) M^{(\alpha)}, the Rényi entropy of the squared Pauli coefficients, measures how spread out those coefficients are. For which Rényi indices does slow OSE growth guarantee that polynomially many terms give accurate expectation values for every input state, and when does fast growth rule it out? Linear growth of M^{(1)}, or power-law growth of M^{(\alpha)} for \alpha>1, forces superpolynomially many terms for a fixed error over all states. Logarithmic growth for 0<\alpha<1/2 guarantees polynomially many terms suffice for every state, and the range is sharp: the operator I-2|0^N\rangle\langle0^N| has bounded OSE for every \alpha\ge1/2 but needs about 2^{N} terms. Averaged over low-average state ensembles the sufficient range extends to 0<\alpha<1. The paper also bounds cumulative error in iterative propagation and fixed-order OTOCs.

Non-unitary quantum butterfly effect: theory and experiment

Sun, 08 Nov 2026 00:00:00 +0000

Out-of-time-order correlators (OTOCs) measure how a local perturbation spreads through a many-body system, and in random unitary circuits they show a ballistic front behind which the signal saturates. Mid-circuit measurements are now routine, but how far and for how long an unread measurement disturbs the rest of a register is poorly characterised. What does the OTOC do when the evolution itself is non-unitary? The authors define an OTOC for quantum channels that bounds how much a perturbation at site y can change a measured expectation value at x. For brickwork Haar-random circuits of qudits measured at each site with probability p per layer, the circuit-averaged OTOC is a transfer-matrix contraction. It decays at late times as \lambda_*^{t} with \lambda_*=1-\tfrac{2(q-1)}{q}Np+O(p^{2}) for Np\ll1, and for sparse measurement in a large system the decay is Gaussian in time with variance 1/(\kappa p). Eight-qubit runs on Quantinuum's H2 resolve the light cone and the decay inside it.

Optimal finite-copy readout of three-qubit entanglement with state retention

Sun, 08 Nov 2026 00:00:00 +0000

Given n copies of an unknown three-qubit pure state, how likely can a fixed measurement be to certify, without false positives, that the state is in the GHZ class (nonzero three-tangle \tau)? How large can the coefficient be in an event whose probability is exactly proportional to \tau^{2}? And can such a certificate leave a copy of the unknown state intact? Fewer than four copies give no certificate. Four copies give optimal probability \tau^{2}/48. Five copies give 5\tau^{2}/72, a factor 10/3 more, and can return the unknown input on success; five is the minimum for that. At six copies certification and exact binary readout first differ: (39+2S)\tau^{2}/296 against \tau^{2}/8, where S is the sum of single-party purities. Local spin measurements with classical communication attain all of these optima.

Certifying quantum code and circuit distances at scale

Sun, 08 Nov 2026 00:00:00 +0000

The circuit distance, the fewest faults in a syndrome-extraction circuit that flip a logical observable without firing any detector, sets the leading order of the logical error rate. For qLDPC circuits with 10^{4} to 10^{5} fault mechanisms, papers usually report upper bounds from heuristic searches, and resource estimates for planned machines rest on assumed values. Can exact distances be certified at that scale? Writing both code and circuit distance as a tropical (min-plus) partition function and combining two dynamic programs, a bounded search and certified relaxations, the method certifies 70 of 74 benchmark instances in the authors' suite against 53 for all other exact solvers combined, and 95 against 80 on an independent benchmark. It certifies codes with up to 31,200 qubits and circuits with up to 8\times10^{5} fault mechanisms. An audit of 26 papers finds overestimated distances in 10, with a gap of at least eight. IBM's two-gross [\![288,12,18]\!] memory circuit has circuit distance 16 with the standard schedule, not 18; other schedules reach 18 at one noisy cycle, at the cost of a ninth timestep per cycle.

Testing gravitationally induced entanglement with massive particles and quantum clocks

Sun, 08 Nov 2026 00:00:00 +0000

Proposed tests of whether gravity can entangle two masses can be explained by the Newtonian potential between fixed masses, which some argue admits a classical, non-local account. A test that needs a relativistic feature of gravity would close that loophole. The contribution of a clock's internal energy to gravitating mass is such a feature, but the entanglement it generates between two clocks takes about 10^{41} s to appear. Replacing one clock by a delocalised levitated particle of about the Planck mass (M\sim10^{-8} kg), and the other by an array of N clocks, shortens the time scale by the particle's mass and by \sqrt N. For N=10^{23} scandium-45 nuclear clocks in a centimetre-scale crystal, 450 µm from a particle delocalised by 0.1 µm, the authors estimate an entanglement (equivalently, dephasing) time of about 5\times10^{6} s, or 64 days (Eq. 9).

Upper and lower bounds for few-copy Gaussian tomography, and the absence of a fermionic warm regime

Sat, 07 Nov 2026 00:00:00 +0000

Learning an m-mode Gaussian state to trace distance \epsilon takes \Theta(m^2/\epsilon^2) copies if all copies can be measured jointly. With one copy at a time, mixed states need more. Chen, Mele, Mele and Preskill showed that for bosons cold states need m^3/\epsilon^2 but warm states only m^2/\epsilon^2. They asked how this temperature crossover looks for finite-dimensional systems. Is there a warm regime for fermions, and what do measurements on blocks of k copies buy? Fermions have no warm regime: for every \beta_0>0, quadratic Gibbs states with \beta\|h\|_F\le\beta_0 need \Theta(m^3/\epsilon^2) single-copy samples at accuracies resolving the ball. At the maximally mixed state, blocks of at most k copies need N>\frac{m^3}{8{,}553{,}600\,k\,\epsilon^2}\qquad(\epsilon\le1/3600). An exact formula shows that the Fisher budget behind this bound is asymptotically attained. Near the vacuum, blocks need \Omega(m^3/(\epsilon^2\min\{\sqrt k,m\})). A particle-number measurement followed by the Nayak–Zhou qudit protocol attains this for every k on number-conserving fermionic and on all cold bosonic Gaussian states.

Extensions of the Haldane gap proof: higher dimensions, near degeneracy, fermions and tensor-network states

Sat, 07 Nov 2026 00:00:00 +0000

A recent paper by OpenAI proved that the spin-one Heisenberg chain is gapped in the thermodynamic limit, using only spectral information from a finite system. The argument, which this paper calls the purity bootstrap, compares the purity of the Gibbs state with that of a dual Gibbs state obtained by exchanging space and imaginary time. Does it work in more than one dimension, for phases with several nearly degenerate ground states, for fermions, and for wave functions rather than Hamiltonians? The bootstrap extends to every spatial dimension: a single finite ratio of partition functions above a fixed threshold certifies a size-independent gap. Summing over symmetry twists lets it handle near degeneracy. Finite calculations show that the 2+1-dimensional transverse-field Ising model for h/J\le1.8 has two low states split by at most Ce^{-cL^2}, and that the toric code in a field with h/J_m\le1/7 has four split by at most Ce^{-cL}, each with a gap above them. A fermionic version establishes a symmetric mass generation phase for t/J\le1/35. For the Jian–Zaletel spin-one PEPS the paper proves a correlation length below 8.012 lattice spacings.

Structured Quantum Hardness from Unstructured Assumptions

Sat, 07 Nov 2026 00:00:00 +0000

Languages in \mathsf{NP}\cap\mathsf{coNP} have short checkable certificates for both answers. The classic candidates for hard ones, factoring and discrete logarithm, fall to Shor's algorithm, and lattice assumptions give certificates only on promise inputs. Bennett and Gill asked whether \mathsf{NP}\cap\mathsf{coNP} stays hard relative to a random oracle. Is there quantum-hard two-sided certification that arises from unstructured sources? If \mathsf{UP}\not\subseteq\mathsf{BQP}, then \mathsf{NP}^{\mathcal O}\cap\mathsf{coNP}^{\mathcal O}\not\subseteq\mathsf{BQP}^{\mathcal O} with probability one over a random oracle \mathcal O. Along the way the paper builds an unbounded-prover NIZK proof for \mathsf{NP} in the quantum random oracle model with no further assumptions. In the other direction, no fully black-box quantum reduction derives a worst-case quantum-hard \mathsf{NP}\cap\mathsf{coNP} problem from post-quantum injective one-way functions and indistinguishability obfuscation.

Information-Spectrum General Formulas for the Capacity Region of Classical-Quantum Multiple Access Channels

Sat, 07 Nov 2026 00:00:00 +0000

Two senders transmit classical messages through a channel whose output is a quantum state. For memoryless channels the capacity region is known, but real channels may have memory or change with block length. The information-spectrum method gives capacity formulas for arbitrary channel sequences: Verdú–Han and Hayashi–Nagaoka for one sender, Han (1998) for the classical two-sender channel. For the classical-quantum multiple access channel only an outer bound (Kubo–Nagaoka 2015) was known. What is the exact region? For every sequence of cq-MACs, the capacity region (vanishing error) is the union over input-distribution sequences of the regions R_1\le\underline I_1, R_2\le\underline I_2, R_1+R_2\le\underline I_0, defined by three spectral inf-mutual information rates. This is the quantum counterpart of Han's formula. For every 0\le\varepsilon<1, the \varepsilon-capacity region equals the 2015 outer bound evaluated at the marginal states, so that bound is tight. Its consistency constraint turns out to be unnecessary.

Exponential mixing time for the Davies dynamics of the quantum random energy model

Sat, 07 Nov 2026 00:00:00 +0000

The quantum random energy model (QREM) puts an independent Gaussian energy of variance n on each of the 2^n computational-basis states and adds a transverse field. In its spin-glass phase, how long does it take to thermalise when weakly coupled to a bath through single-qubit Pauli operators? Lower bounds on mixing times for noncommuting random Hamiltonians were listed as open, because their eigenbasis, and hence the Davies jump operators, is not explicitly known. For every \beta>\beta_c=\sqrt{2\log2} and every field 0\le\Gamma<\Gamma_c(\beta), where e^{\beta\beta_c}=2\cosh(\beta\Gamma_c), the Davies mixing time satisfies \liminf_n\frac1n\log T_{\rm mix}\ge c_{\rm mix}>0 almost surely. This holds for any detailed-balance rates whose maximum grows subexponentially, with or without dephasing terms, and without assuming primitivity.

Provable circuit-level thresholds for non-abelian topological phases

Sat, 07 Nov 2026 00:00:00 +0000

Abelian topological codes such as the toric code have shallow syndrome circuits and decoders with proven thresholds. Non-abelian phases could offer more powerful logical gates, but outside a few "solvable" cases (D_4, S_3) there was no explicit syndrome-extraction circuit and no circuit-level threshold proof. Earlier work on the double-Fibonacci phase gave only numerics under simplified noise. Can every non-chiral 2D topological phase serve as a fault-tolerant memory under realistic noise? For every non-chiral bosonic topological order given by a Turaev–Viro state sum, the paper constructs a local circuit that extracts syndromes and applies corrections. It pairs the circuit with a polynomial-time clustering decoder that runs on the fly. Under local stochastic circuit-level noise with rate below a constant threshold \epsilon_*, the logical error probability decays quasi-stretched-exponentially in the system size L. The paper also sketches how the scheme extends to logical gates built from defects.

Asymptotic advantage of quantum one-way and SMP communication for total functions

Fri, 06 Nov 2026 00:00:00 +0000

For partial functions, with a promise on the inputs, quantum one-way communication can be exponentially cheaper than classical. For total functions, defined on every input, the question is how large a gap can be at all. Is there a total Boolean function with a polynomial gap between bounded-error quantum and randomised communication in the one-way and simultaneous-message (SMP) models, with public randomness allowed? Yes. Alice holds M\in\mathbb F_2^{d\times d} and Bob holds u,z\in\mathbb F_2^d, with input length n=d^2+2d. Let F_d(M;u,z)=1 exactly when (M+M^{\mathsf T})u=z and u^{\mathsf T}Mu=0. Then Q^{\parallel}(F_d) and Q^{\to}(F_d) are \Theta(\sqrt n), while R^{\to}(F_d) and R^{\parallel}(F_d) are \Theta(n). With 2d shared EPR pairs, a classical SMP protocol costs O(\sqrt n), and any entanglement still leaves \Omega(\sqrt n).

Frustration-freeness is decidable but unprovable

Fri, 06 Nov 2026 00:00:00 +0000

A translation-invariant nearest-neighbour Hamiltonian on an L\times L square lattice, with positive semidefinite bond terms of zero ground energy, is frustration-free if a single state is annihilated by every term. For one fixed L this is a finite linear-algebra question. Physics usually wants the answer for every L. Is that question decidable when the local dimension d is fixed? Fixing d does not settle it on its own: the spectral-gap problem is undecidable on the same inputs. For each d there is a single size L(d), the same for every Hamiltonian, such that frustration-freeness on the L(d)\times L(d) lattice implies it at every size (Theorem 1), so the problem is decidable for each fixed d. Yet, if ZFC is consistent, there is an explicit Hamiltonian with diagonal, commuting terms that is frustration-free at every size although ZFC cannot prove it (Theorem 3). The two fit together because no algorithm computes a valid cutoff for every d (Theorem 4); the cutoff grows at least like the busy-beaver function, L(am+b)\ge\mathrm{BB}(m).

Fidelity Determines the Minimum Error of Quantum Recovery

Fri, 06 Nov 2026 00:00:00 +0000

A recovery after noise can be judged by its worst-input entanglement fidelity F, the probability of passing a test that the state and its entanglement with a reference survived. It can also be judged by its operational error D=\tfrac12\|\Phi-\mathrm{id}\|_\diamond, the largest change in any measurement probability. In general 1-F\le D\le\sqrt{1-F}. For a fixed noise channel and encoding, do the two coincide once each is optimised over recoveries? Holdsworth, Singh and Wilde proved equality when encoder and decoder share free randomness, and left the unassisted case open. They coincide. For every finite-dimensional channel \Phi there is an output unitary U with 1-F(\mathrm{Ad}_U\Phi)\le D(\mathrm{Ad}_U\Phi)\le1-F(\Phi)\le D(\Phi), so over any family of recoveries closed under final unitaries, including Kraus-rank caps, \inf D=1-\sup F. The unitary is the polar part of the Kraus combination weighted by the worst input's amplitudes. The paper also gives a semidefinite program for the best final unitary when the error is below one half, formulas for recovery with a retained noise record, and robustness bounds. In a three-qubit calibration example the optimal correction has 20.3 percent lower operational error than the recovery that maximises average gate fidelity.

Quantum trajectory of a spin oscillator, continuous retrodiction beyond the Heisenberg uncertainty relation

Fri, 06 Nov 2026 00:00:00 +0000

The Heisenberg relation \Delta x\,\Delta p\ge1/2 limits how well a state predicts the outcomes of measuring two conjugate observables. It says nothing about guesses of a past measurement made with data from both before and after it. Can continuous monitoring of a macroscopic spin oscillator retrodict x, p and every rotated quadrature at once with variances below the standard quantum limit, and can this be kept up over long runs? In a paraffin-coated ^{87}Rb vapour cell with about 5.17\times10^{10} atoms, alternating stroboscopic QND measurements of \hat x_A and \hat p_A at rate \kappa^2\eta=2\pi\times1002 Hz were analysed forwards, with the state \rho(t), and backwards, with the effect matrix E(t). Prediction alone gave variances 0.88 dB above the standard quantum limit. Combining past and future data gave both variances 1.01\pm0.15 dB below it, so \Delta x\,\Delta p beat the Heisenberg value, and this held over 1.4 hours. Rotating the verification phase gave sub-SQL retrodicted variances for every quadrature, 0.388\pm0.025 on average against 0.5.

Quantum Advantage with Sign-Free Proofs: An Oracle Separation between StoqMA and MA

Fri, 06 Nov 2026 00:00:00 +0000

In \mathsf{StoqMA} the verifier receives a quantum witness, uses ancillas in |0\rangle and |+\rangle, applies only classical reversible gates (X, CNOT, Toffoli) and makes one Hadamard-basis measurement. The class sits between \mathsf{MA} and \mathsf{AM}, and if it admitted error reduction it would equal \mathsf{MA}. Its complete problems concern stoquastic, sign-problem-free Hamiltonians, where quantum Monte Carlo often works. Does this nearly classical verifier beat every classical \mathsf{MA} verifier, at least relative to an oracle? Yes. There is a classical XOR oracle \mathcal O with \mathsf{StoqMA}^{\mathcal O}\ne\mathsf{MA}^{\mathcal O} (Theorem 1.1). The separating problem asks whether a sparse, high-girth graph on 2^m vertices, given by a randomly relabelled adjacency-list oracle, has top eigenvalue at least n or at most 4\sqrt n. The verifier receives the Perron eigenvector and runs a Hadamard test that accepts with probability 1/2+\langle\psi|A|\psi\rangle/(2d). That is at least 3/4 for the YES graph and at most 1/2+1/\sqrt n for every NO graph. No \mathsf{MA} verifier with a polynomial witness and polynomially many queries can do this.

Polynomial-time classical simulation of boson and fermion sampling under thermal loss

Fri, 06 Nov 2026 00:00:00 +0000

Photonic sampling experiments lose a constant fraction of their particles. Does a fixed loss rate already make Haar-random boson or fermion sampling classically easy, without assuming that loss grows with system size, that outputs are dilute, or that circuits are shallow? Earlier simulation results each needed one of those extra conditions. For Fock-state boson sampling, Gaussian boson sampling with fixed uniform squeezing and fermion sampling with four-mode magic inputs, under thermal loss at any fixed transmissivity \eta<1 (pure loss included), there is a classical sampler with error \varepsilon in total variation, with probability 1-\delta over Haar-random interferometers, in time polynomial in m, 1/\varepsilon and 1/\delta (Theorem III.1). If the ideal output is only polynomially flat, \chi^2(\rho_U\|\tau)\le m^{O(1)}, the time is (m/\varepsilon)^{O(\log(m/\varepsilon))} for any interferometer. It becomes polynomial when loss acts after each of \Omega(\log m) layers. Near full input filling, the noisy output is close to one fixed distribution, whatever the interferometer.

Algorithmic Wave-Particle Duality: Pathfinding in Welded Trees is Hard