You Don’t Need New Hardware

Plain-language explainer for doi:10.5281/zenodo.21480501 (#639)

The access problem

The Raven ISA operates in the complex-β plane: β = σ + it/ℏ with σ ≠ 0. This is PT-symmetric, non-Hermitian quantum mechanics. Every quantum computer built today operates on the imaginary-β axis: unitary evolution e^{−iH₀t} with β = it/ℏ exactly. The non-Hermitian dynamics — where exceptional points live, where EP sensing works, where gain-loss competition creates the H¹/H² tier boundary — appear to be inaccessible.

This paper proposes three practical routes to simulate Raven ISA dynamics on standard qubit hardware, with honest resource accounting.

The β landscape

β value Physics ISA tier Accessible on QC?
β → ∞ (real) Classical, argmax H⁰ ORBIT Yes (classical)
β finite, real Thermal/MGE H¹ TWIST Partial
β = it/ℏ Quantum mechanics H¹ TWIST Yes (all QC)
β = σ + it, σ ≠ 0 PT-symmetric / Raven H² Proposed here

Three paths

Path A — Lindblad + postselection

Couple the n-qubit system to an ancilla qubit. Evolve the joint system unitarily via a Hamiltonian engineered so that tracing out the ancilla gives the desired non-Hermitian evolution on the system. Postselect on the ancilla outcome that corresponds to “no jump” — the trajectory where the non-Hermitian evolution occurred.

Success probability: exp(−‖Γ‖t) where ‖Γ‖ is the gain-loss strength and t is time. For strong dissipation or long times, this is exponentially small.

✓ Works on any hardware today. ✓ Exactly correct (not approximate).
✗ Exponential overhead. ✗ Not scalable beyond short times.

Path B — Naimark dilation

Embed the n-qubit non-Hermitian Hamiltonian H into a 2n-qubit Hermitian Hamiltonian H̃ via Stinespring dilation. The PT-symmetric dynamics run in the physical subspace; the ancilla n qubits are the “bath” degrees of freedom. The exceptional point structure is preserved in the dilation.

✓ Polynomial overhead (doubles qubit count). ✓ Full state vector is accessible.
✗ Requires 2× qubit count. ✗ Naimark embedding can be non-trivial to construct.

Path C — Classical probability reweighting (advocated)

Run standard unitary circuits. For each shot, multiply the measured energy E by the Boltzmann-like weight w = exp(−σ · E) and renormalise classically. This recovers the non-Hermitian expectation value ⟨O⟩_{β=σ+it} without additional qubits or postselection. Works for any observable O that can be measured on the Hermitian circuit.

✓ Works today on IBM, IonQ, Quantinuum. ✓ No qubit overhead. ✓ Scalable.
✗ Gives observables only, not the full non-Hermitian state. ✗ Statistical noise scales as exp(2σ·‖E‖)/N_shots — requires more shots for large σ or large energy range.

Hardware roadmap

Year Capability Raven ISA tier
2026 Classical reweighting on 100-qubit systems S = 0 EP sensing
2027 Naimark dilation on 20+20 qubits S = 1 tier crossing
2028 Native Lindblad control (trapped ion) Full Raven ISA
2030 PT-symmetric photonic + classical hybrid HPU-P substrate
2035 Dedicated non-Hermitian processor Autonomous Raven

The 5-qubit example

A 5-qubit transverse-field Ising model with complex transverse field h = h₀ + iγ (where γ is the gain-loss rate) was simulated via Path C on a classical simulator. The exceptional point at γ = h₀ was located by tracking eigenvalue coalescence as (h₀, γ) varied.

PiTch number S = 1 confirmed: one loop around the EP in (h₀, γ)-space exchanges the two lowest eigenvalue sheets. Full resource accounting: 200 shots at each of 50 (h₀, γ) grid points. Reweighting recovered EP location to within 2% of exact.

The postselection caveat

Path A’s exponential postselection cost is the same overhead that cancels the claimed EP search speedup (see PtEpSearch). This paper makes no claim that Raven ISA provides query complexity advantages — the argument is purely about simulation fidelity. EP sensing in the classical regime (no postselection) remains valid.

See also