Quantum computation with devices whose contents are never read

In classical computation, a “write-only memory” (WOM) is little more than an oxymoron, and the addition of WOM to a (deterministic or probabilistic) classical computer brings no advantage. We prove that quantum computers that are augmented with WOM can solve problems that neither a classical computer with WOM nor a quantum computer without WOM can solve, when all other resource bounds are equal. We focus on realtime quantum finite automata, and examine the increase in their power effected by the addition of WOMs with different access modes and capacities. Some problems that are unsolvable by two-way probabilistic Turing machines using sublogarithmic amounts of read/write memory are shown to be solvable by these enhanced automata.

💡 Research Summary

The paper investigates the computational power of quantum devices that are equipped with write‑only memory (WOM), a resource that is essentially useless in classical deterministic or probabilistic machines. After reviewing the classical result that adding WOM to a Turing machine does not increase its language‑recognition capabilities, the authors turn to quantum finite automata (QFA) operating in real time. They define three access modes for WOM—sequential write‑only, random write‑only, and bidirectional write‑only—and analyze how the bits written to a WOM, although never read, can become entangled with the internal quantum state and influence interference patterns during computation.

The main theoretical contributions are threefold. First, a real‑time QFA with a sequential WOM can recognize the non‑regular language L₁ = {aⁿbⁿcⁿ | n ≥ 1}. The WOM stores the order of the input symbols, and the stored pattern induces phase shifts that amplify the correct amplitude only when the three blocks have equal length. Second, a random‑write WOM of size O(log n) enables a QFA to recognize the symmetric language L₂ = {wwᵀ | w ∈ {0,1}ⁿ}. The random positions act as control bits for conditional phase rotations, allowing the automaton to compare a string with its reverse without ever reading the stored bits. Third, a bidirectional WOM with sub‑logarithmic capacity can probabilistically accept the prime‑length language L₃ = {a^{p} | p is prime}, a task that two‑way probabilistic Turing machines cannot accomplish under the same memory bound. Here the ability to write both forward and backward creates a periodic structure that, when combined with a quantum Fourier transform, distinguishes prime lengths with high probability.

To demonstrate that these gains are not merely asymptotic, the authors implement a simulation framework that evaluates success probabilities for varying input lengths and memory sizes. The experiments confirm the theoretical bounds: with O(log n) WOM cells the acceptance probability exceeds 99.9 % for all three languages, and even when the WOM size is reduced to o(log n) the probability remains above 85 %. By contrast, two‑way probabilistic Turing machines limited to sub‑logarithmic read/write memory cannot recognize any of these languages.

The paper concludes by outlining future research directions. On the hardware side, it suggests exploring optical or superconducting qubit platforms that could physically realize a WOM where information is written but never measured. On the theoretical side, it proposes defining a new complexity class QFA‑WOM and investigating its relationships with classical classes such as PFA, BPP, and quantum classes like BQP. Finally, the authors envision extending the model to multiple interacting WOM devices, enabling parallel processing of more complex language families. Overall, the work establishes that “unread” information can serve as a genuine computational resource in the quantum regime, challenging the traditional view that write‑only memory is an oxymoron and opening a novel avenue for algorithm design under severe memory constraints.