Dismagicker: Unitary Gate for Non-Stabilizerness Reduction

Abstract

We introduce the notion of dismagicker: non-Clifford unitary gate designed to reduce the non-stabilizerness (also called magic) of quantum many-body states. Although both entanglement and non-stabilizerness are fundamental quantum resources, they require distinct control strategies. While disentanglers (unitary operations that lower entanglement) are well-established in tensor network methods, analogous concept for non-stabilizerness suppression has been largely missing. In this work, we define dismagicker as non-Clifford unitary operation that actively suppresses non-stabilizerness, steering states toward classically simulatable stabilizer states. We develop optimization method for constructing dismagickers within the Matrix Product States framework. Our numerical results show that the non-stabilizerness reduction procedure, when combined with entanglement reduction steps with Clifford circuits, significantly improves the accuracy for both classical simulation of many-body systems and quantum state preparation on quantum devices. Dismagicker enriches our toolkit for the manipulation of many-body states by unifying non-stabilizerness and entanglement reduction.

Figures (3)

• Figure 1: Schematic of the interleaved optimization flow of dismagicker and Clifford disentangler on a MPS. At each step of the sweep, a local two-site tensor $|\phi\rangle_{k,k+1}$ is targeted. We first apply a parameterized dismagicker gate $U_{\mathcal{M}}$ to minimize the non-stabilizerness. Immediately following this, a two-site Clifford disentangler $U_C$ is applied to the intermediate state $U_{\mathcal{M}}|\phi\rangle$ to actively suppress the entanglement entropy without altering the non-stabilizerness. Finally, a Singular Value Decomposition (SVD) is performed to update the local tensors, after which the algorithm moves to the next pair of sites to continue the sweep.
• Figure 2: The reduction of $M_2$ (a) and EE (b) with different strategies. The protocol transitions from a dismagicker phase (sweeps 1–6) to a Disentangler phase (sweeps 6–10) for the red and green results. Joint optimization ($U_C U_{\mathcal{M}} \rightarrow U_C$, green) achieves significantly deeper simultaneous suppression of both resources compared to sequential ($U_{\mathcal{M}} \rightarrow U_C$, red) or Clifford-only ($U_C$, blue) strategies. Results are averaged over $1000$ random initial $N=6$ states. Highly entangled stabilizer states are first generalized by applying a depth-6 circuit consisted of random two-qubit Clifford circuits to a product state. Then non-stabilizerness is injected by applying three additional layers of Haar-random two-qubit unitary gates to this intermediate state. Standard deviations are represented by the shadow.
• Figure 3: Result from the joint optimization of dismagicker and Clifford disentangler of the 1D Heisenberg chain ground state with size $L=20$. The initial state is an MPS with bond dimension $D=4$ from DMRG. (a) Evolution of $M_2$ and EE versus optimization sweeps. The dismagicker $U_{\mathcal{M}}$ is selected by sampling $200$ random Clifford+$R_z(\theta)$ gate combinations, with $M_2$ evaluated via sampling from $10^4$ shots PhysRevLett.131.180401. (b) Relative error $|E - E_\text{exact}|/|E_\text{exact}|$ of the ground-state energy. At each step, a DMRG calculation restricted to $D=4$ is performed on the effectively transformed Hamiltonian, demonstrating rapid convergence to a much higher accuracy than the initial DMRG result.