Analysis of Error Propagation in Quantum Computers

• URL: http://arxiv.org/abs/2209.01699v1
• Date: Sun, 4 Sep 2022 21:45:15 GMT
• Title: Analysis of Error Propagation in Quantum Computers
• Authors: Ziang Yu and Yingzhou Li
• Abstract summary: Most quantum gate errors can be characterized by two error models, namely the probabilistic error model and the Kraus error model. We prove that for a quantum circuit with either of those two models or a mix of both, the propagation error in terms of Frobenius norm is upper bounded by $2(1 - (1 - r)m)$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Most quantum gate errors can be characterized by two error models, namely the probabilistic error model and the Kraus error model. We proved that for a quantum circuit with either of those two models or a mix of both, the propagation error in terms of Frobenius norm is upper bounded by $2(1 - (1 - r)^m)$, where $0 \le r < 1$ is a constant independent of the qubit number and circuit depth, and $m$ is the number of gates in the circuit. Numerical experiments of synthetic quantum circuits and quantum Fourier transform circuits are performed on the simulator of the IBM Vigo quantum computer to verify our analytical results, which show that our upper bound is tight.

Related papers

• Reshaping quantum device noise via quantum error correction [0.818005422059368]
  We show that quantum error correction codes can reshape the native noise profiles of quantum devices. We analytically derive the quantum channels describing noisy two-qubit entangling gates. We then demonstrate the noise reshaping on the IonQ Aria-1 quantum hardware.
  arXiv  Detail & Related papers  (2024-11-01T17:20:04Z)
• Exponential separation in quantum query complexity of the quantum switch with respect to simulations with standard quantum circuits [1.151731504874944]
  We prove that the action of the quantum switch on two $n$-qubit quantum channels cannot be simulated deterministically. This demonstrates an exponential separation in quantum query complexity of indefinite causal order compared to standard quantum circuits.
  arXiv  Detail & Related papers  (2024-09-27T03:18:28Z)
• Scalable quantum circuits for exponential of Pauli strings and Hamiltonian simulations [0.0]
  We design quantum circuits for the exponential of scaled $n$-qubit Pauli strings using single-qubit rotation gates, Hadamard gate, and CNOT gates. A key result we derive is that any two Pauli-string operators composed of identity and $X$ gates are permutation similar. We apply these circuit models to approximate unitary evolution for several classes of Hamiltonians using the Suzuki-Trotter approximation.
  arXiv  Detail & Related papers  (2024-05-22T12:57:09Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Normal quantum channels and Markovian correlated two-qubit quantum errors [77.34726150561087]
  We study general normally'' distributed random unitary transformations. On the one hand, a normal distribution induces a unital quantum channel. On the other hand, the diffusive random walk defines a unital quantum process.
  arXiv  Detail & Related papers  (2023-07-25T15:33:28Z)
• Quantum Error Correction with Gauge Symmetries [69.02115180674885]
  Quantum simulations of Lattice Gauge Theories (LGTs) are often formulated on an enlarged Hilbert space containing both physical and unphysical sectors. We provide simple fault-tolerant procedures that exploit such redundancy by combining a phase flip error correction code with the Gauss' law constraint.
  arXiv  Detail & Related papers  (2021-12-09T19:29:34Z)
• $i$-QER: An Intelligent Approach towards Quantum Error Reduction [5.055934439032756]
  We introduce $i$-QER, a scalable machine learning-based approach to evaluate errors in a quantum circuit. The $i$-QER predicts possible errors in a given quantum circuit using supervised learning models. It cuts the large quantum circuit into two smaller sub-circuits using an error-influenced fragmentation strategy.
  arXiv  Detail & Related papers  (2021-10-12T20:45:03Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Sample Complexity of Learning Quantum Circuits [4.329298109272386]
  We prove that physical quantum circuits are PAC learnable on a quantum computer via empirical risk minimization. Our results provide a valuable guide for quantum machine learning in both theory and experiment.
  arXiv  Detail & Related papers  (2021-07-19T18:00:04Z)
• Fault-tolerant Coding for Quantum Communication [71.206200318454]
  encode and decode circuits to reliably send messages over many uses of a noisy channel. For every quantum channel $T$ and every $eps>0$ there exists a threshold $p(epsilon,T)$ for the gate error probability below which rates larger than $C-epsilon$ are fault-tolerantly achievable. Our results are relevant in communication over large distances, and also on-chip, where distant parts of a quantum computer might need to communicate under higher levels of noise.
  arXiv  Detail & Related papers  (2020-09-15T15:10:50Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.