Application of Quantum Tide Theory in Quantum Computing: Noise-Topological Stability Effects and Verifiable Predictions

In recent experiments, time-dependent periodic fields are used to create exotic topological phases of matter with potential applications ranging from quantum transport to quantum computing. These non-equilibrium states, at high driving frequencies, exhibit the quintessential robustness against local disorder that is also seen at equilibrium. However, the existence of topological stability under a general setting is an open problem. We propose an effective theory that leverages on modern free probability theory and ideas in random matrices to analytically capture the existence of the topological phase for finite driving frequencies and across a range of disorder. We predict that, depending on the strength of disorder, such systems may be gapped (topological) or gapless (trivial). The theory can be used to predict properties of the transition between the two phases including the critical point. We corroborate our results by comparing to exact diagonalization for driven-disordered 1D Kitaev chain and 2D Bernevig-Hughes-Zhang (BHZ) models.In recent experiments, time-dependent periodic fields are used to create exotic topological phases of matter with potential applications ranging from quantum transport to quantum computing. These non-equilibrium states, at high driving frequencies, exhibit the quintessential robustness against local disorder that is also seen at equilibrium. However, the existence of topological stability under a general setting is an open problem. We propose an effective theory that leverages on modern free probability theory and ideas in random matrices to analytically capture the existence of the topological phase for finite driving frequencies and across a range of disorder. We predict that, depending on the strength of disorder, such systems may be gapped (topological) or gapless (trivial). The theory can be used to predict properties of the transition between the two phases including the critical point. We corroborate our results by comparing to exact diagonalization for driven-disordered 1D Kitaev chain and 2D Bernevig-Hughes-Zhang (BHZ) models.

Mar 22, 20180 citations

Quantum Computing and Quantum Topology

Louis Hirsch Kauffman, Samuel J. Lomonaco

Chapman & Hall/CRC applied mathematics and nonlinear science seriesSep 19, 20070 citations

Efficient quantum process tomography for Clifford circuits

Shichuan Xue, Guang-Yao Huang, Yong Liu +7 more

A Clifford circuit is a pivotal tool in quantum computing and has extensive applications in quantum error correction codes and topological quantum computing. Hence, it is essential to benchmark and verify the effect of Clifford circuits against noise and errors. Standard quantum process tomography is a fundamental technique for fully characterizing quantum dynamics, but at the cost of exponential time, space, and computation with an increasing number of qubits. Here, we propose an efficient quantum process tomography method for Clifford circuits. Combining with the stabilizer formalism, we prove theoretically that, for an $n$ -qubit Clifford circuit, our method merely needs $m$ ancillary qubits and $\ensuremath{\lceil}n/m\ensuremath{\rceil}$ input stabilizer states to obtain the quantum process. Numerical simulation results show that our method could perfectly rebuild the unknown Clifford quantum circuit with fidelity over $99.99%$ to six qubit cases. Our work provides an efficient and practical approach to benchmark and verify Clifford circuits.A Clifford circuit is a pivotal tool in quantum computing and has extensive applications in quantum error correction codes and topological quantum computing. Hence, it is essential to benchmark and verify the effect of Clifford circuits against noise and errors. Standard quantum process tomography is a fundamental technique for fully characterizing quantum dynamics, but at the cost of exponential time, space, and computation with an increasing number of qubits. Here, we propose an efficient quantum process tomography method for Clifford circuits. Combining with the stabilizer formalism, we prove theoretically that, for an $n$-qubit Clifford circuit, our method merely needs $m$ ancillary qubits and $\ensuremath{\lceil}n/m\ensuremath{\rceil}$ input stabilizer states to obtain the quantum process. Numerical simulation results show that our method could perfectly rebuild the unknown Clifford quantum circuit with fidelity over $99.99%$ to six qubit cases. Our work provides an efficient and practical approach to benchmark and verify Clifford circuits.

Physical Review ASep 20, 20232 citations

Quantum simulations with noisy quantum computers

Jay Gambetta

Bulletin of the American Physical SocietyMar 13, 20170 citations

Distinctive predictions and theorems of the Quantum Tide Theory

wangchao

Sep 25, 20260 citations

Reduction of Theoretical Uncertainty in Quantum Computing

Hideaki Matsueda, David W. Cohen

International Journal of Theoretical PhysicsFeb 1, 19994 citations

n

-qubit Clifford circuit, our method merely needs

m

ancillary qubits and $\ensuremath{\lceil}n/m\ensuremath{\rceil}$ input stabilizer states to obtain the quantum process. Numerical simulation results show that our method could perfectly rebuild the unknown Clifford quantum circuit with fidelity over

99.99%

to six qubit cases. Our work provides an efficient and practical approach to benchmark and verify Clifford circuits.