Simulating quantum noise by enlarging the quantum system

Making room for irreversible behavior

A quantum computer’s gates are unitary: mathematically, their action can be reversed. Yet many processes researchers want to simulate are not reversible when only the system of interest is considered. A qubit can lose energy, a measurement can change its state, and interactions with an environment can destroy coherence.

Quantum channels provide a mathematical language for these transformations. They preserve total probability and keep quantum states physically valid, including when the system is entangled with another system.

In Quantum Simulation of Quantum Channels and Applications, an arXiv preprint posted on November 9, 2026, Lúcio S. Fassarella develops a unified presentation of how to implement such channels using a larger quantum circuit. The paper combines established theory with a proposed construction for approximating Markovian dynamics: evolution whose next step depends on the current state rather than additional information about its history.

The auxiliary-system trick

The starting point is the Choi–Kraus representation, which expresses a channel through a collection of operators describing its possible contributions. Fassarella uses these operators to construct a Stinespring dilation, then extends that construction to a unitary transformation.

In practical terms, the circuit adds auxiliary qubits, called ancillas, prepared in a known state. Gates act jointly on the system and ancillas. Ignoring the ancillas afterward recovers the desired channel on the system alone.

The apparent irreversibility therefore comes from considering only part of a larger system. The combined transformation remains reversible, while information can pass into the auxiliary register.

This is established quantum theory, not a newly discovered way around quantum mechanics. The paper’s purpose is to organize the construction and several applications within one framework, termed the unitary-dilation, or UD, strategy.

Two demonstrations of the shared framework

The first application prepares mixed states, which describe statistical mixtures rather than a single pure quantum state. The construction starts from the target state’s eigenvectors and their probabilities. Ancilla-controlled transformations produce a larger pure state whose system component has the required mixture when the ancilla is disregarded—a purification of the target state.

For a single-qubit example, the target mixes the plus and minus states with probabilities two-thirds and one-third. Fassarella reports an observable’s simulated mean of 1.668124, close to the theoretical value of approximately 1.6667.

The second application concerns generalized measurements, described by positive operator-valued measures, or POVMs. Coupling the system to an ancilla allows an ordinary projective measurement on the enlarged system to reproduce the generalized measurement’s outcome probabilities. This recovers the established idea of Naimark dilation.

In a two-outcome example, the reported simulated probabilities are approximately 0.93384 and 0.06616, compared with theoretical probabilities of 0.93301 and 0.06699. Both demonstrations used Qiskit’s AerSimulator, rather than physical quantum hardware.

An Euler-like approach to quantum dynamics

The paper’s proposed contribution addresses open-system evolution governed by a Lindblad equation. This equation combines Hamiltonian motion with dissipative processes such as energy loss.

A straightforward first-order time step resembles the Euler method for ordinary differential equations: use the current rate of change to estimate the next state. However, a truncated approximation must also satisfy the conditions required of a quantum channel.

Fassarella introduces a residual operator into the small-step Kraus construction. Its contribution begins at second order in the time step, leaving the desired first-order dynamics unchanged. Solving a quadratic operator equation enforces the normalization condition needed for trace preservation; the Kraus form supplies complete positivity.

Repeatedly applying the resulting channel approximates the evolution without splitting the evolution into a Trotter product. A single-qubit amplitude-damping example compares simulated energy evolution with an exact solution; the author reports reasonable agreement over 20 steps.

What remains unresolved

Avoiding Trotterization does not establish a computational speedup. The method remains first-order: the paper estimates a local error proportional to the squared time step and an accumulated error proportional to the time step for fixed simulation duration.

There are also resource costs. Ancillas can be recycled if a device supports intermediate measurement and reinitialization, reducing auxiliary storage, but this does not remove the gate cost of repeated transformations.

Most importantly, the residual equation still has to be solved. The worked damping example uses a specially chosen operator form; a general solution procedure is left for future research. The demonstrations are small simulator examples, not evidence of large-scale hardware performance. The preprint thus offers a unified construction and illustrative results, rather than an established efficiency advantage.