Quantum error mitigation for rotation symmetric bosonic codes with symmetry expansion

• URL: http://arxiv.org/abs/2211.06164v2
• Date: Fri, 2 Dec 2022 12:35:34 GMT
• Title: Quantum error mitigation for rotation symmetric bosonic codes with symmetry expansion
• Authors: Suguru Endo, Yasunari Suzuki, Kento Tsubouchi, Rui Asaoka, Kaoru Yamamoto, Yuichiro Matsuzaki, Yuuki Tokunaga
• Abstract summary: We propose a class of quantum error mitigation that virtually projects the state onto the noise-free symmetric subspace. We show that symmetry expansion dramatically suppresses the effect of photon loss. Our novel error mitigation method will significantly enhance computation accuracy in the near-term bosonic quantum computing paradigm.
• Score: 0.2770822269241974
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The rotation symmetric bosonic code (RSBC) is a unified framework of practical bosonic codes that have rotation symmetries, such as cat codes and binomial codes. While cat codes achieve the break-even point in which the coherence time of the encoded qubits exceeds that of unencoded qubits, with binomial codes nearly approaching that point, the state preparation fidelity needs to be still improved for practical quantum computing. Concerning this problem, we investigate the framework of symmetry expansion, a class of quantum error mitigation that virtually projects the state onto the noise-free symmetric subspace by exploiting the system's intrinsic symmetries and post-processing of measurement outcomes. Although symmetry expansion has been limited to error mitigation of quantum states immediately before measurement, we successfully generalize symmetry expansion for state preparation. To implement our method, we use an ancilla qubit and only two controlled-rotation gates via dispersive interactions between the bosonic code states and the ancilla qubit. Interestingly, this method also allows us to virtually prepare the RSBC states only from easy-to-prepare states, e.g., coherent states. We also discuss that the conventional symmetry expansion protocol can be applied to improve the computation fidelity when the symmetries of rotation bosonic codes are unavailable due to low measurement fidelity. By giving comprehensive analytical and numerical arguments regarding the trace distance between the error-mitigated state and the ideal state and the sampling cost of quantum error mitigation, we show that symmetry expansion dramatically suppresses the effect of photon loss. Our novel error mitigation method will significantly enhance computation accuracy in the near-term bosonic quantum computing paradigm.

Related papers

• Efficient quantum algorithms for testing symmetries of open quantum systems [17.55887357254701]
  In quantum mechanics, it is possible to eliminate degrees of freedom by leveraging symmetry to identify the possible physical transitions. Previous works have focused on devising quantum algorithms to ascertain symmetries by means of fidelity-based symmetry measures. We develop alternative symmetry testing quantum algorithms that are efficiently implementable on quantum computers.
  arXiv  Detail & Related papers  (2023-09-05T18:05:26Z)
• Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits [0.0]
  We consider quantum circuits in one and two dimensions comprising randomly applied unitary gates and local measurements. In the absence of randomness, the protocol generates a symmetry-protected long-range entangled state in a finite-depth circuit. We find two important time scales that we associate with the emergence of certain symmetry generators.
  arXiv  Detail & Related papers  (2023-06-22T16:09:12Z)
• Experimental realization of deterministic and selective photon addition in a bosonic mode assisted by an ancillary qubit [50.591267188664666]
  Bosonic quantum error correcting codes are primarily designed to protect against single-photon loss. Error correction requires a recovery operation that maps the error states -- which have opposite parity -- back onto the code states. Here, we realize a collection of photon-number-selective, simultaneous photon addition operations on a bosonic mode.
  arXiv  Detail & Related papers  (2022-12-22T23:32:21Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
  We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
  arXiv  Detail & Related papers  (2021-12-27T21:15:35Z)
• Analytical and experimental study of center line miscalibrations in M\o lmer-S\o rensen gates [51.93099889384597]
  We study a systematic perturbative expansion in miscalibrated parameters of the Molmer-Sorensen entangling gate. We compute the gate evolution operator which allows us to obtain relevant key properties. We verify the predictions from our model by benchmarking them against measurements in a trapped-ion quantum processor.
  arXiv  Detail & Related papers  (2021-12-10T10:56:16Z)
• Near-optimal covariant quantum error-correcting codes from random unitaries with symmetries [1.2183405753834557]
  We analytically study the most essential cases of $U(1)$ and $SU(d)$ symmetries. We show that for both symmetry groups the error of the covariant codes generated by Haar-random symmetric unitaries, typically scale as $O(n-1)$ in terms of both the average- and worst-case distances against erasure noise.
  arXiv  Detail & Related papers  (2021-12-02T18:46:34Z)
• Surface Code Design for Asymmetric Error Channels [55.41644538483948]
  We introduce a surface code design based on the fact that bit flip and phase flip errors in quantum systems are asymmetric. We show that, compared to symmetric surface codes, our asymmetric surface codes can provide almost double the pseudo-threshold rates. As the asymmetry of the surface code increases, the advantage in the pseudo-threshold rates begins to saturate for any degree of asymmetry in the channel.
  arXiv  Detail & Related papers  (2021-11-02T10:41:02Z)
• Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements [58.720142291102135]
  We analyze the error-correction capabilities of rotation-symmetric codes using a teleportation-based error-correction circuit. We find that with the currently achievable measurement efficiencies in microwave optics, bosonic rotation codes undergo a substantial decrease in their break-even potential.
  arXiv  Detail & Related papers  (2021-08-02T16:12:13Z)
• All-optical Quantum State Engineering for Rotation-symmetric Bosonic States [0.0]
  We propose and analyze a method to generate a variety of non-Gaussian states using coherent photon subtraction. Our method can be readily implemented with current quantum photonic technologies.
  arXiv  Detail & Related papers  (2021-05-23T22:43:23Z)
• Quantum Error Mitigation using Symmetry Expansion [0.0]
  Noise remains the biggest challenge for the practical applications of any near-term quantum devices. We develop a general framework named symmetry expansion which provides a wide spectrum of symmetry-based error mitigation schemes. We show that certain symmetry expansion schemes can achieve a smaller estimation bias than symmetry verification.
  arXiv  Detail & Related papers  (2021-01-08T18:30:48Z)

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.