On a chain of exchange-coupled quantum dots a Heisenberg exchange pulse of area pi is a SWAP, so the parallel bubble-sort SWAP network of superconducting chains is native to exchange-only (EO) spin qubits, and any other pulse area fuses routing with an entangling interaction. We build a variational "bubble-sort exchange network" (odd-even transposition, one parameter per pulse) and study it as a Born machine read out by Pauli spin blockade. Exchange conserves total spin, so the reachable readout distributions are fixed by the total-spin content of the initial product state. For the two-spin singlet-triplet encoding we derive a selection rule -- outcomes with k triplet pairs are bounded by the initial weight in sectors S <= k (S = 0 excluded for k = 1) -- and prove by a transportation argument that it is also sufficient: the reachable distributions form the polytope cut out by the rule, and its total-variation floor is attained. Products of singlets and T0's forbid whole outcome classes; the Neel state forbids none; the three-spin EO code has no floor. We then distil, in noise-free simulation, next-token distributions of GPT-2 over restricted vocabularies into the network, with matrix-product-state (MPS) Born machines as classical control. At six logical qubits the three-spin chain reaches KL = 0.011 nat at depth N and 0.004 at 2N, below the bond-dimension-4 MPS; the two-spin chain from the Neel state reaches 0.014 at 2N and 0.004 at 3N, against 0.28-1.5 from singlet/triplet products for the first teacher. Final states lie largely outside the code space: leakage is a resource, not an error. No arrangement of disjoint pulses meets every pair in fewer than N-1 rounds, and at depth 2N the chain distils as well as a 2D array or non-local couplings. Sector-restricted simulation extends this to 10-14 logical qubits (up to 30 dots).
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19 pages, 9 figures, 7 tables. Code and data: https://github.com/minatoyuichiro/eoall-check
On a chain of exchange-coupled quantum dots a Heisenberg exchange pulse of area pi is a SWAP, so the parallel bubble-sort SWAP network of superconducting chains is native to exchange-only (EO) spin qubits, and any other pulse area fuses routing with an entangling interaction. We build a variational "bubble-sort exchange network" (odd-even transposition, one parameter per pulse) and study it as a Born machine read out by Pauli spin blockade. Exchange conserves total spin, so the reachable readout distributions are fixed by the total-spin content of the initial product state. For the two-spin singlet-triplet encoding we derive a selection rule -- outcomes with k triplet pairs are bounded by the initial weight in sectors S <= k (S = 0 excluded for k = 1) -- and prove by a transportation argument that it is also sufficient: the reachable distributions form the polytope cut out by the rule, and its total-variation floor is attained. Products of singlets and T0's forbid whole outcome classes; the Neel state forbids none; the three-spin EO code has no floor. We then distil, in noise-free simulation, next-token distributions of GPT-2 over restricted vocabularies into the network, with matrix-product-state (MPS) Born machines as classical control. At six logical qubits the three-spin chain reaches KL = 0.011 nat at depth N and 0.004 at 2N, below the bond-dimension-4 MPS; the two-spin chain from the Neel state reaches 0.014 at 2N and 0.004 at 3N, against 0.28-1.5 from singlet/triplet products for the first teacher. Final states lie largely outside the code space: leakage is a resource, not an error. No arrangement of disjoint pulses meets every pair in fewer than N-1 rounds, and at depth 2N the chain distils as well as a 2D array or non-local couplings. Sector-restricted simulation extends this to 10-14 logical qubits (up to 30 dots).
We consider the ``transport'' of the state of a spin across a Heisenberg-coupled spin chain via the use of repeated SWAP gates, starting with one of two states---one in which the leftmost spin is down and the others up, and one in which the leftmost two spins are in a singlet state (i.e., they are entangled), and the others are again all up. More specifically, we transport the state of the leftmost spin in the first case and the next-to-leftmost spin in the second to the other end of the chain, and then back again. We accomplish our SWAP operations here by increasing the exchange coupling between the two spins that we operate on from a base value J to a larger value JSWAP for a time $t=\ensuremath{\pi}\ensuremath{\hbar}/4{J}_{\text{SWAP}}$. We determine the fidelity of this sequence of operations in a number of situations---one in which only nearest-neighbor coupling exists between spins and there is no magnetic dipole-dipole coupling or noise (the most ideal case), one in which we introduce next-nearest-neighbor coupling, but none of the other effects, and one in which all of these effects are present. In the last case, the noise is assumed to be quasistatic, i.e., the exchange couplings are each drawn from a Gaussian distribution, truncated to only nonnegative values. We plot the fidelity as a function of JSWAP to illustrate various effects, namely crosstalk due to coupling to other spins, as well as noise, that are detrimental to our ability to perform a SWAP operation. Our theory should be useful to the ongoing experimental efforts in building semiconductor-based spin quantum computer architectures.
Standard universal quantum computing using exchange-only qubits typically requires three physical spins per logical qubit, leading to significant hardware overhead. Conversely, two-spin units offer higher density but rely on local magnetic field gradients for control, increasing integration complexity. In this paper, we propose a resource-efficient quantum machine learning (QML) architecture that achieves high expressibility using minimal two-spin units and Heisenberg exchange interactions alone, without any magnetic gradients. We shift the paradigm from universal gate-based control to utilizing the intrinsic, time-domain dynamics of a spin chain as a learning resource. Numerical simulations on MNIST digit classification demonstrate that the symmetry-protected constraints of isolated spin pairs are bypassed by leveraging inter-pair exchange coupling. This interference-mediated state mixing significantly enhances the expressibility of the Hilbert space. The model reaches a test-set accuracy of 90.9% +/- 0.2% over five independent seeds on the full 10,000-image MNIST test set. Under an identical linear readout, the trained quantum feature map (88.1%) clearly outperforms a classical linear baseline on the same PCA inputs (83.2%) as well as an untrained (reservoir-style) version of the same dynamics (53.0%), demonstrating that the learned, input-dependent exchange pulses implement a genuinely non-linear and trainable feature map. The protocol is also robust to experimentally relevant imperfections: accuracy remains at 89.9% under 10% quasi-static pulse-area noise and at 89.8% when every observable is estimated from 10^3 measurement shots. These findings suggest that competitive QML can be executed on the simplest possible semiconductor spin-chain hardware, bypassing the need for leakage-prone encodings or complex micro-magnet integration.
Ground states of Sachdev-Ye-Kitaev (SYK)-type models are volume-law entangled, which makes them costly both for tensor networks and for quantum hardware simulations. Thus, it remains unclear where quantum hardware could outperform classical simulation of such models. In this work, we study a spin SYK-dot chain, in which q dense SYK dots of p qubits are joined by single ZZ bonds of strength K. The entanglement across any cut is then bounded by floor(p/2) ln 2 plus the inter-dot entanglement, and the two-qubit depth of one Trotter step is set by p alone. A resource estimate shows that a quantum advantage for the ground state could appear only for dots of about 15 to 21 qubits or more. There, a single Trotter step already requires two-qubit error rates of order 10^{-6}, beyond the reach of noisy intermediate-scale quantum (NISQ) hardware. We test the assumptions of this estimate with an imaginary-time matrix product state (MPS) that applies each dot as one block. It agrees with exact diagonalisation at (p, q) = (6, 2). At (5, 2), a variational circuit with the same dot-plus-link layout comes within 3.6% of the exact energy, and noisy simulations show that its fidelity decays as assumed in the resource estimate. At (8, 5), i.e., N = 40 qubits, the energy converges at bond dimension chi = 768, far below the exact value 2^20, and the inter-dot entanglement stays small and is set mainly by K. Out-of-time-order correlators across the links decay on a time scale that shrinks rapidly with |K|. Thus, the dot size p and the inter-dot coupling K together set the entanglement of the chain, and with it where a quantum advantage could appear.
We propose a symmetry-adapted eigensolver for strongly correlated systems that separates where the wave function is \emph{sampled} from where it is \emph{defined}. The lattice is divided into equal blocks: parallel quantum circuits absorb the entanglement within each block, while a matrix product state (MPS) backbone bridges the blocks and restores global correlations. The resulting real-space amplitude ϕ(areal) acts only as a sample generator---configurations are drawn from ∣ϕ(areal)∣2 directly, block by block, without any Markov chain. The variational state itself is defined in a symmetry-adapted basis by two separate rules: the modulus of ψ(asymm) is the square root of the total weight accumulated over the entire equivalence class, p(asymm)=∑areal∈{garepr}∣ϕ(areal)∣2, whereas its phase is inherited from the single representative amplitude ϕ(arepr). The modulus rule is what makes the scheme both exact and cheap: the distributionp(asymm) sampled in the symmetric basis is exactly the one induced by the mapping from the real-space distribution p(areal), so every generated configuration is an unbiased sample of ∣ψ(asymm)∣2; the phase rule then fixes the only freedom that remains. Because amplitudes within a class are combined in probability rather than summed with symmetry characters, ψ is \emph{not} a group projection of the circuit-MPS state; the class-wide aggregation instead supplies long-range, symmetry-enforced entanglement that the MPS never has to carry itself.
One should not assume that reconstructing an electronic observable with a smaller set of measurement settings will cut the number of repetitions in proportion. Each setting is simply a basis change and qubit readout, but the savings are not guaranteed to be commensurate. Take two electrons of opposite spin in two spatial orbitals: the orbital degree of freedom of each electron acts as a logical qubit and rotations are independent in the spin sectors. From the observable's one- and two-qubit coefficients we derive an exact floor for the setting count and a decomposition to meet it in no more than three settings. With fewer settings, the minimum error in the two-qubit correlation coefficients is set by the singular values left out. A case in point is an exchange with equal nonzero couplings on the three Pauli axes. This demands three orbital settings yet only one joint measurement. We offer a Clifford circuit for four physical qubits to effect the necessary mapping of Pauli products under conjugation. In the case of a one-parameter family of logical singlet-triplet mixtures, the orbital-to-Clifford shot cost ratio is three at maximum mixing and trends toward 3/2 near the logical singlet. Where spin sectors may be mixed, isotropic exchange needs one orbital setting. For spin-conserving Hamiltonians with N spatial orbitals encoded via Jordan-Wigner, the X-rank, the binary rank of the X parts of its strings, of any commuting Pauli string family is no more than 2(N−1). Searches with the Robust Adaptive Nature-inspired Global Explorer (RANGE) reach this limit for CH4, with the rank of the Hamiltonian support vouching for the maximality of the search values. And for all nonidentity Pauli strings on n qubits, semidefinite witnesses from the Lovász theta number give a lower bound on the Clifford setting count that agrees with the integer cover and counting bounds at 2n+1.
Abstract In conventional exchange-only (EO) spin qubit demonstrations, quantum gates have been implemented using sequences of individually pulsed pairwise exchange interactions with only one exchange coupling active at a time. Alternatively, multiple non-commuting exchange interactions can be pulsed simultaneously, reducing circuit depths and providing protection against leakage. We demonstrate high-fidelity quantum control of an always-on exchange-only (AEON) qubit, operated using simultaneous exchange pulses in a triangular quantum dot (QD) array. We use blind randomized benchmarking to characterize the performance of the full AEON single-qubit Clifford gate set, achieving an average Clifford gate fidelity F C1 = 99.86%. Extensions of this work may enable more efficient EO two-qubit entangling gates as well as the implementation of native i -Toffoli gates in Loss-DiVincenzo single-spin qubits.