One-bit post-training quantization represents each weight using only its sign, requiring all deployment contexts to share the same binary weight matrix even when their activation statistics favor different sign patterns. We study this shared-sign constraint and introduce Quantum Random Access Quantization (QRAQ). This framework encodes context-dependent signs in a quantum random-access code and retrieves them via context-matched Pauli measurements. Under an explicit fresh-copy logical readout model, QRAQ produces an unbiased, context-specific binary surrogate with a tractable shot-noise penalty. We prove a row-wise separation from shared-sign one-bit PTQ with signed per-row scales. When the optimal context-wise signs are incompatible, QRAQ achieves a strictly lower ideal reconstruction risk. We also derive finite-shot and calibrated-noise conditions under which this separation is retained. Fixed-readout quantum schemes are classically simulable, so the relevant resource in this model is measurement incompatibility rather than quantization alone. Finally, we characterize the role of scale granularity, provide finite-sample certificates, and evaluate the predicted ideal, finite-shot, noisy, and multi-context regimes in simulator experiments.
One-bit post-training quantization represents each weight using only its sign, requiring all deployment contexts to share the same binary weight matrix even when their activation statistics favor different sign patterns. We study this shared-sign constraint and introduce Quantum Random Access Quantization (QRAQ). This framework encodes context-dependent signs in a quantum random-access code and retrieves them via context-matched Pauli measurements. Under an explicit fresh-copy logical readout model, QRAQ produces an unbiased, context-specific binary surrogate with a tractable shot-noise penalty. We prove a row-wise separation from shared-sign one-bit PTQ with signed per-row scales. When the optimal context-wise signs are incompatible, QRAQ achieves a strictly lower ideal reconstruction risk. We also derive finite-shot and calibrated-noise conditions under which this separation is retained. Fixed-readout quantum schemes are classically simulable, so the relevant resource in this model is measurement incompatibility rather than quantization alone. Finally, we characterize the role of scale granularity, provide finite-sample certificates, and evaluate the predicted ideal, finite-shot, noisy, and multi-context regimes in simulator experiments.
Qubit-efficient quantum relaxations compress classical decision variables into expectation values on substantially fewer qubits. We ask what resource tradeoffs this compression entails for quantum optimization. For the complete quadratic-Majorana encoding of m=Θ(n2) binary variables on~n qubits, we define the universal margin as the smallest correlator magnitude that can be guaranteed with prescribed signs for every target sign (bit) assignment. We show that it is exactly ΔMaj(n)=tan(4nπ)=Θ(1/n), whereas uniformly random sign assignments retain Θ(1/n) target-specific margins. Arbitrary density operators and mixed fermionic Gaussian states generate the same quadratic-Majorana covariance body, so non-Gaussian state resources cannot enlarge this two-point relaxation. More generally, standard quantum random access code bounds provide general information-theoretic baselines. For any fixed family of m designated binary observables on~n qubits, the universal margin is at most (2ln2n/m), and random access decoding from N copies with constant success probability above 1/2 requires nN=Ω(m). For a fixed Pauli correlation encoding required to work uniformly over all targets, maintaining a fixed nonzero decoded magnitude under smooth sign decoding therefore requires a rescaling parameter that grows as the available margin shrinks. Thus, while providing substantial qubit savings, compression can shift cost into restricted expectation value geometry, smaller expectation value magnitudes, or more demanding information recovery rather than eliminate it.
Quantum executions sharing a provenance record can produce different output distributions. We ask which execution details to retain, and at what precision, to guarantee agreement within a declared Hellinger tolerance. Under a specified channel model, we combine independent stochastic mechanisms and coherent rotation differences to certify recording precision without output simulation or explicit dependence on register dimension. For four-qubit quantum approximate optimization at depth one, a 13-bit comparison record suffices at tolerance 0.05 over a declared continuous noise range, uniformly in programmed angles for each fixed task. Pairwise separation constraints characterize sufficient field sets on finite context classes, exposing omissions that pass individually but fail jointly. Separately, six-qubit hardware measurements over six tested contexts certify minimum label counts of two for raw outputs and one after a fixed decoder, at tolerance 0.15 with 97\% simultaneous confidence under stationary independent shots. Execution records thereby carry checkable agreement guarantees.
Quantum random access codes (QRACs) enable multiple classical bits to be encoded into fewer qubits, while allowing only a selected bit to be retrieved with probability greater than the corresponding classical limit. Here, we use 2→1 and 3→1 QRACs for simultaneous transmission of multiple binary images through a single quantum data stream. At the receiver, the measurement choice determines which encoded image is reconstructed, while the remaining image information is disturbed by the measurement process. The inherent correct-bit probabilities of these QRACs are approximately 85.4% and 78.9%, respectively. By applying median and morphological filtering to the decoded binary images, we improve the reconstruction accuracy in an image-dependent manner, reaching 99.17% for 2→1 QRACs and 98.36% for 3→1 QRACs. We also analyze the effect of depolarizing noise on reconstruction quality using accuracy, peak signal-to-noise ratio, and structural similarity index measure. These results demonstrate a selective-access framework for QRAC-based image transmission with potential applications in controlled image/video transmission.
Compressed quantum encodings aim to overcome hardware limitations towards tackling challenging problems at scale, with many classical variables mapped onto noncommuting observables of fewer qubits. Classically, relaxations such as the semidefinite program formulation of MaxCut trade solution quality for computational efficiency. By contrast, quantum relaxations based on compression can amplify the worst-case complexity of the problem being solved. We study quantum random access optimization (QRAO), a special case of the Pauli correlation encoding (PCE) framework that assigns up to three binary variables to the Pauli X, Y, and Z observables of each qubit, with the packing choices determining the compressed Hamiltonian to be optimized. We identify explicit QRAO optimal energy promise problems complete for NP, StoqMA, and QMA, with inverse-polynomial promise gaps for the latter two. Our problem reductions preserve inverse-polynomial promise gaps without requiring gadgets or ancillas. For any prescribed packing, we show that weighted MaxCut instances compress, up to a known shift and rescaling, to arbitrary nonnegative-weight pairwise Pauli couplings allowed by the packing. For QRAO, using one aligned axis gives an NP-complete energy problem. Using two or three positive aligned Pauli axes generally gives QMA-complete problems, with bipartite restrictions in BQP ∩ StoqMA.
We show that this computational hardness survives compilation and is practically relevant. Notably, this result applies directly to the current QRAO compiler implementation in Qiskit Optimization 0.7.0, confirming our hardness results are not artifacts of artificial or contrived packing rules. Altogether our results identify worst-case complexity barriers arising from quantum compression, while making no broad claims about typical cases or the performance and trainability of algorithm pipelines that use it.
An n↦pm random access code (RAC) is an encoding of n bits into m bits such that any initial bit can be recovered with probability at least p , while in a quantum RAC (QRAC), the n bits are encoded into m qubits. Since its proposal, the idea of RACs was generalized in many different ways, e.g. allowing the use of shared entanglement (called entanglement-assisted random access code, or simply EARAC) or recovering multiple bits instead of one. In this paper we generalize the idea of RACs to recovering the value of a given Boolean function f on any subset of fixed size of the initial bits, which we call f -random access codes. We study and give protocols for f -random access codes with classical ( f -RAC) and quantum ( f -QRAC) encoding, together with many different resources, e.g. private or shared randomness, shared entanglement ( f -EARAC) and Popescu-Rohrlich boxes ( f -PRRAC). The success probability of our protocols is characterized by the noise stability of the Boolean function f . Moreover, we give an upper bound on the success probability of any f -QRAC with shared randomness that matches its success probability up to a multiplicative constant (and f -RACs by extension), meaning that quantum protocols can only achieve a limited advantage over their classical counterparts.
A binary (n, m) quantum random access code (QRAC) compresses an n-bit classical string into an m-qubit quantum state, from which a decoder attempts to recover a randomly selected target bit.Of particular interest is the optimal average probability of success, P Q,avg,opt n,m .The square-root expression 1 2 + 1 2 m/n was conjectured to upper-bound this quantity, and recent constructions of (n, n -1) QRACs by Suzuki and (n, n -2) QRACs by Akibue et al. meet it exactly.In this work, we prove that these constructions are optimal, thereby determining P Q,avg,opt n,n-1 and P Q,avg,opt n,n-2 .The proof uses the local-to-global reconstruction framework of Lin and de Wolf, based on the pretty good measurement (PGM), together with dimensional and positive-semidefinite (PSD) constraints on the induced channel.Based on these constraints, we also derive an efficient linear-programming (LP) converse for general binary (n, m) QRACs.We evaluate this converse in closed form for two infinite parameter families and prove that it is strictly tighter than Akibue et al.'s bound at every point in those families except (n, m) = (3, 1), where the two coincide.