Every major quantum programming language restricts to unitary operations and Hermitian Hamiltonians. This is understandable: unitarity is tractable, elegant, and sufficient for standard gate-model quantum computing. But real quantum systems are open, dissipative, and non-Hermitian. By refusing to engage with loss, the field is in a bind -- unable to express PT-symmetric computation, Lindblad dynamics, exceptional-point algorithms, or even the classical limit of quantum mechanics. We identify the missing primitive: BIND (the Frobenius comultiplication delta: A -> A tensor A), and the missing parameter: beta (the semiring grade interpolating between tropical, quantum, and PT-symmetric regimes). The Raven ISA is the minimal non-unitary extension of the Heunen et al. phase language that adds these two ingredients. It implements five computational advantages unavailable to unitary languages, and subsumes all existing quantum programming languages as the beta = i special case. It is time to find BIND.
Every major quantum programming language restricts to unitary operations and Hermitian Hamiltonians. This is understandable: unitarity is tractable, elegant, and sufficient for standard gate-model quantum computing. But real quantum systems are open, dissipative, and non-Hermitian. By refusing to engage with loss, the field is in a bind -- unable to express PT-symmetric computation, Lindblad dynamics, exceptional-point algorithms, or even the classical limit of quantum mechanics. We identify the missing primitive: BIND (the Frobenius comultiplication delta: A -> A tensor A), and the missing parameter: beta (the semiring grade interpolating between tropical, quantum, and PT-symmetric regimes). The Raven ISA is the minimal non-unitary extension of the Heunen et al. phase language that adds these two ingredients. It implements five computational advantages unavailable to unitary languages, and subsumes all existing quantum programming languages as the beta = i special case. It is time to find BIND.
The Raven ISA tier (β∈ℂ, PT-symmetric) is shown to be accessible on any existing quantum computer via a hybrid classical-quantum protocol: standard unitary circuits supply the imaginary-β quantum phases, while classical post-measurement reweighting by Boltzmann factors e^(−σE_k) supplies the real-β dissipation. The composite estimator reconstructs the complex-β partition function Z(σ+it) with no additional qubits, no postselection overhead, and gate cost identical to a standard Meld circuit. Three application classes are demonstrated: RavenRank (dissipation-weighted ranking), PT-symmetric eigensolvers for non-Hermitian matrices, and exceptional-point search with sub-Grover query complexity.
We introduce the Hot Processing Unit (HPU), a unified programming model for dissipative quantum hardware. Five physically distinct substrate classes -- PT-symmetric photonic chips (HPU-P), bosonic cat qubits (HPU-B), radical-pair molecular processors (HPU-R), non-Hermitian electrical circuits (HPU-C), and exceptional-point (EP) sensor arrays (HPU-E) -- share a common computational structure: they execute programmes in which gain, loss, and complex inverse temperature beta are first-class operations. We show that the Raven Instruction Set Architecture (ISA) is the natural HPU instruction set, with SNAP-count (the number of tier-promotion events) as the resource metric analogous to T-count in fault-tolerant quantum computing. The GPU unified diverse parallel hardware under CUDA; the HPU unifies diverse dissipative hardware under the Raven ISA. We present the HPU architecture, a five-substrate compiler pipeline, and five benchmark algorithms -- culminating in the observation that EP sensing (SNAP-count = 0) is the first demonstrated HPU algorithm, and that autonomous quantum error correction on cat qubits is the route to Shor's algorithm on HPU hardware.
Quantum computing has been, from its inception, a programme of refrigeration: isolate the system, suppress dissipation, drive the physical temperature toward zero. This programme has achieved remarkable results, and the researchers who built it deserve full credit. But it is incomplete. Real quantum systems are open. Biology runs its most precise quantum computations -- kinetic proofreading, photosynthetic energy transfer, avian magnetoreception -- in warm, wet, dissipative environments, not in dilution refrigerators. Exceptional-point sensors already outperform classical sensors by exploiting, rather than suppressing, gain and loss. We coin the term hot quantum computing for computation that treats dissipation as a resource rather than a defect, and we describe the instruction set architecture -- the Raven ISA, built on the Motive ISA -- that gives it a rigorous programming model. Hot quantum is not noisy quantum: the distinction is between a leaky pipe (still trying to be airtight) and a water wheel (working because of the flow). The field has been jumping out of the bath. It is time to embrace it.
Non-Hermitian (NH) quantum systems demonstrate striking differences from their Hermitian counterparts, leading to claims of NH advantage in areas ranging from metrology to entanglement generation. We show that in the context of quantum computation, any such NH advantage is unlikely to be scalable as an efficient computational resource: If coherent nonunitary evolution with renormalization could be realized with only polynomial overhead, then the resulting model could implement postselection, implying implausibly strong complexity-theoretic power under standard assumptions. We define NHBQP ( U ) as the computational power of polynomial-size quantum circuits that, in addition to a standard universal unitary gate set, may apply a fixed gate U on O ( 1 ) qubits that is not proportional to a unitary, with the state renormalized after each use of U . We prove that this model is powerful enough to decide every language in PostBQP (equivalently PP ). Moreover, in the standard uniform circuit-family model, this characterization is tight: For any fixed such nonunitary gate U , NHBQP ( U ) = PostBQP = PP . PostBQP is believed intractable, so this suggests that any scalable NH computational advantage must come with a compensating cost limiting its efficiency. Additionally, we study simulation complexity of restricted classes of nonunitary systems by purifying them to postselected unitary evolution in a form preserving system locality. Using this framework, we show that unitary gates with postselection can simulate not only evolution under NH Hamiltonians but arbitrary quantum trajectories. Any NH model whose purification lies in a strongly simulable unitary family (e.g., Clifford, matchgate, or low-bond-dimension tensor-network circuits) remains efficiently classically simulable, provided the relevant postselected events occur with probability Ω ( 2 − poly ( n ) ) . Thus, adding non-Hermiticity to a universal unitary system makes it infeasibly computationally powerful, while adding it to a strongly simulable system adds no computational power in this setting.
Heunen, Lemonnier, McNally, and Rice (POPL 2026) introduce the phase language: two primitives, Ph(theta) and 'if let p then s', that together are universal for unitary quantum computation. Their language is elegant and expressive, yet by design it restricts to unitary operations, to a fixed real-phase semiring, and to a single computational tier. We show that the phase language is the grade-beta=i special case of the Origami instruction-set architecture (ISA), a beta-graded Frobenius monad defined over the beta-semiring. Three main results are proved. Theorem 1 (restricted embedding): the phase-only and empty-pattern fragment of the phase language embeds faithfully into the H^1-tier subcategory of Origami_{beta=i} generated by ORBIT, TWIST, and FLIP. Theorem 2 (strict extension): the Raven ISA (complex beta) is strictly more expressive than the phase language; any computation using a non-unitary TWIST serves as witness. Theorem 3 (Frobenius monad): the quadruple {ORBIT, FLIP, BIND, MERGE} forms a Frobenius monad in the PROP semantics, satisfying the Frobenius condition and giving a categorical foundation for the full ISA. The graded structure enables a three-tier computational hierarchy: tropical (beta -> infinity), quantum (beta = i), and PT-symmetric (beta in C), with the phase language occupying exactly the middle tier.
Quantum information processing holds immense promise, but its practical implementation is fundamentally challenged by dissipation, the irreversible loss of information and energy to the environment. The conventional approach treats dissipation as an obstacle to overcome, typically through resource-intensive quantum error correction. Such schemes impose overheads of orders of magnitude in terms of both qubits and operations. This creates significant space, control and time costs, making near-term practical implementation highly challenging. This thesis adopts a different viewpoint, harnessing dissipation for quantum algorithms. We explore the design, application, and conceptual advantages of dissipative quantum algorithms. We establish the foundational tools for this approach by demonstrating how to engineer a universal set of nonunitary operations using intrinsic, controllable dissipation. We present a hardware-efficient method, experimentally realized in a trapped-ion system, for implementing any two-qubit Markovian quantum channel without requiring ancilla qubits or measurements. This provides a practical and versatile toolbox for constructing dissipative algorithms on near-term quantum devices. Building on this, we apply these tools to an inherently dissipative task: the preparation of thermal states. We introduce a variational quantum-classical algorithm that integrates engineered nonunitary operations with unitary gates. By leveraging weak symmetries of the target Hamiltonian, we design efficient ansätze that significantly improve the fidelity of state preparation. Finally, we address one of the most significant barriers to scaling variational quantum algorithms: the prevalence of barren plateaus, where optimization gradients vanish exponentially with system size. We prove that dissipative algorithms, by incorporating periodic qubit resets, can mitigate both noise-induced and unitary barren plateaus. This mechanism allows for a class of scalable computations that are intractable for purely unitary approaches in the presence of noise. Together, these results demonstrate that dissipation is not just a source of error, but a powerful resource. By systematically developing the necessary operations, applying them to relevant problems, and identifying fundamental scalability advantages, this work showcases dissipative quantum computing as a compelling avenue in quantum information processing.