Harnessing Intrinsic Noise for Quantum Simulation of Open Quantum Systems

TL;DR

This paper addresses the challenge of simulating open quantum systems on quantum computers by reframing intrinsic hardware noise as a resource rather than a drawback. It introduces a noise-assisted, ancilla-free framework that partially encodes a system's decoherence channels into Pauli strings and leverages the device's own noise to realize nonunitary dynamics, with an error bound derived from the Choi–Jamiołkowski isomorphism. The method applies across single- and two-qubit channels and scales to multiple qubits with adaptive encoding, yielding decoherence-free subspace clusters that further support efficient open-system simulation. Benchmarks against classical simulations of exciton transport demonstrate close agreement, highlighting practical potential on NISQ hardware and guiding hardware co-design to maximize physical-to-logical qubits. This work thus offers a viable path toward early quantum advantage in simulating dissipative quantum dynamics with reduced error-correction overhead.

Abstract

Simulating open quantum systems on quantum computers presents a fundamental challenge: open quantum dynamics are intrinsically nonunitary, whereas quantum computers operate through unitary evolution. Conventional approaches overcome this mismatch by encoding nonunitary processes into unitary circuits, but such methods incur substantial overhead in both qubits and gates. Here, we propose an alternative perspective. Quantum processors are themselves open systems, inherently subject to noise. Instead of correcting all errors and then encoding nonunitary dynamics with unitary logical qubits and gates, we show how noise can be harnessed as a computational resource. We develop a noise-assisted quantum algorithm that selectively preserves physical noise to emulate nonunitary channels, enabling efficient simulation of open quantum dynamics with minimal qubit requirements. Our approach applies both to noisy intermediate-scale quantum (NISQ) devices and future fault-tolerant architectures. By leveraging intrinsic noise, this method circumvents the need to encode nonunitary dynamics into unitary gates and relaxes fidelity requirements on physical qubits, thereby reducing the overhead of quantum error correction. This framework reframes noise from a limitation into a resource, opening new directions for practical quantum simulation of open systems

Figures (5)

• Figure 1: a) 1D braiding structure with $n=d+1$. b) 3D braiding with the ${Y}_1{I}_2$ nodal channel. This braiding generates a decoherence-free subspace for the exemplified $\{{Y}_1{I}_2, {I}_1{Y}_2, {X}_1{Z}_2, {Z}_1{X}_2\}$ system channels under the $\{{X}_1{X}_2,{Y}_1{Y}_2,{Z}_1{Z}_2\}$ channels. Blue arrows indicate mapped channels; yellow arrows indicate alternate choices that preserve the DFS while maintaining the $n=d+1$ structure. c) The simplest example of the braiding structure $((n,d)), n>d$. Here $n=4, d=2.$ This does not generate an all-to-all mapping since the absence of ${Y}_1{Y}_2$ does not close the DFS. The black arrows in each subfigure denote the branches emerging out of a selected node and highlight the braiding dimension.
• Figure 2: a) Extension of the 1D braiding to multiple qubits. This figure shows the formation of mutually exclusive subclusters under the same intrinsic noise $XX$ for two examples of encoded circuits. b) Extension of the 3D braiding showing cluster formation by the system channels under the presence of three intrinsic noise channels, $\left\{{X}_1{X}_2, {Y}_1{Y}_2, {Z}_1{Z}_2\right\}$. This assumes identical nearest-neighbor gate implementations.
• Figure 3: Examples of two-qubit partially encoded gates: (a) (Nearest-neighbor gates) An example of how the encoded nodal channel $ZZ..Z$ is transformed under the two-qubit intrinsic noise $XX$. (b–c) Two examples of circuits where the nearest-neighbor gate implementation is relaxed. This gives rise to encoded Pauli strings that are different from those obtained in (a) under the same intrinsic noise $XX$.
• Figure 4: convergence of the partial encoding algorithms: a) Simultaneous convergence of the residuals for the $XY$ and $IY$ system channels when $XY$ is explicitly encoded (inset). b) Explicitly encoding $IY$ likewise drives simultaneous convergence of both channels. In both a) and b), the residuals of the other $16$ channels remain negligible, indicating that under $XX$ intrinsic noise the $XY$ and $IY$ channels map into each other and define a decoherence-free subspace. c) Similar convergence behavior is observed for the set $\{YI, ZX, IY, XZ\}$ in the presence of intrinsic noise $\{XX, YY, ZZ\}$; over-encoding manifests as residuals diverging to large negative values. d) An adaptive scheme that selects which system channel to encode at each step—here choosing $XZ$ and $ZX$ (insets omitted for clarity)—yields improved convergence of residuals toward zero.
• Figure 5: Benchmarking our algorithm on exciton transport. (a) Two coupled excitons model with $\{XZ, IY\}$ decoherence channels. The dotted lines denote analytical calculations, and the solid lines denote the quantum circuit evolution using partial encoding. b) shows a similar analysis for $\{ZZ, YY\}$ decoherence channels. In both a) and b), the intrinsic hardware noise channels are $\{XX, II\}$, and analytical and noise-assisted simulations are in close agreement. c) Here we extend the intrinsic noise $\{XX, YY, ZZ\}$ to encode the $\{XZ, IY, ZX, YI\}$ bath channels of the system. d) Extension to four nearest-neighbor coupled excitons with system decoherence channels $\{XZXZ, IYIY, IYXZ, XZIY\}$ under intrinsic noise $\{XX, II\}$. Our noise-assisted simulations closely match analytical predictions; minor deviations stem from Trotterization of the Hamiltonian's nearest-neighbor terms.

Theorems & Definitions (1)

• Theorem 1