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Raven on Existing Hardware: Simulating PT-Symmetric Quantum Dynamics via Hybrid Classical-Quantum Reweighting

Ian Richard C Buckley

Published Jul 22, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.21480501

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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.
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.
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.
Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as 'the quantum variational eigensolver' was developed (Peruzzo et al 2014 Nat. Commun. 5 4213 ) with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through a relaxation of exponential operator splitting. We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we show how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.
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.
Digital quantum computers promise exponential speedups in performing quantum time-evolution, providing an opportunity to simulate quantum dynamics of complex systems in physics and chemistry. However, the task of extracting desired quantum properties at intermediate time steps remains a computational bottleneck due to wavefunction collapse and no-fast-forwarding theorem. Despite significant progress towards building a Fault-Tolerant Quantum Computer (FTQC), there is still a need for resource-efficient quantum simulators. Here, we propose a hybrid simulator that enables classical computers to leverage FTQC devices and quantum time propagators to overcome this bottleneck, so as to efficiently simulate the quantum dynamics of large systems initialized in an unknown superposition of a few system eigenstates. It features no optimization subroutines and avoids barren plateau issues, while consuming fewer quantum resources compared to standard methods when many time steps are required.