Source-linked AI summary
A simplify proposal for realizing multiqubit tunable phase gate in circuit QED
Wen-An Li
TL;DR
As qubit counts grow, decomposing multiqubit gates into elementary gates becomes increasingly complicated, while gates involving more than three qubits have not been experimentally implemented. The scheme combines quantum Zeno dynamics with asymmetric encoding to implement a one-step gate using a pulse on the central qudit, without individual addressing or frequency adjustments. At 3π/g, the system returns to its initial state with an additional phase π; |δg1(2)| = 10%g causes a fidelity reduction smaller than 3%.
Problem
As qubit counts grow, decomposing multiqubit gates into elementary gates becomes increasingly complicated, while gates involving more than three qubits have not been experimentally implemented.
Source: §I · pp. 1–2Method
The scheme combines quantum Zeno dynamics with asymmetric encoding to implement a one-step gate using a pulse on the central qudit, without individual addressing or frequency adjustments.
Source: §I · p. 2, §II · p. 3Results
At 3π/g, the system returns to its initial state with an additional phase π; |δg1(2)| = 10%g causes a fidelity reduction smaller than 3%.
Source: §III · pp. 6–7Takeaways & Limitations
The scheme provides a tunable phase gate in the non-resonant case and a faster π-phase gate in the resonant case.
Source: §V · p. 9
Abstract
from arXiv · showhide
We propose a scheme to realize multiqubit tunable phase gate in a circuit QED setup where two resonators each coupling with a qudit are interconnected to a common qudit (d = 4). In this proposal, only two levels of each qudit serve as the logical states and other two levels are used for the gate realization. The proposal is efficient and simple because it requires only one step, no adjustments of the qudit level spacings and resonator mode frequency are needed during the whole process. Only a classical microwave pulse is needed to drive the central coupler qudit, no matter how many qudits involve, which significantly reduces experimental difficulty. In non-resonant case, the tunable phase gate can be achieved readily, while under the resonant condition a π-phase gate can be realized after a full cycle of Rabi oscillation where the gate speed is rather fast due to the resonant interaction. We have shown that the resulting effective dynamics allows for the creation of high fidelity phase gate. The influence of various decoherence processes such as the decay of the resonator mode, and the relaxation of the qudits is investigated. Moreover, the proposed scheme can be easily generalized to realize N-qubit phase gate.
I. INTRODUCTION
Multiqubit gates are needed in quantum algorithms and error-correction protocols, but decomposing them into elementary gates becomes increasingly complicated as qubit counts grow. The paper proposes a one-step tunable phase gate designed to avoid several implementation demands of earlier schemes.
I. INTRODUCTION
- Multiqubit gates are used in quantum algorithms and error-correction protocols, while decomposing them into elementary gates becomes increasingly complicated as qubit counts grow.The introduction identifies direct realization as a needed approach.Source: §I · p. 1
- A multiqubit controlled phase gate shifts the phase of one state component and supports quantum algorithms, quantum Fourier transforms, error correction, and Toffoli implementation.The cited applications are marked [5],,, respectively.Source: §I · p. 1
- The introduction notes that decomposed Toffoli gates require longer execution and yield lower overall fidelities, while gates above three qubits remain experimentally unimplemented.The paper frames these as constraints motivating direct multiqubit gate realization.Source: §I · pp. 1–2
- Earlier proposals require multiple operational steps or individual qubit addressing, and one cited one-step scheme provides only a π-phase gate rather than a tunable phase.The seven-step three-qubit implementation and 2n + 1-step n-qubit procedure are described for Yang et al; Zhang et al proposed the one-step but non-tunable scheme.Source: §I · p. 2
- The proposed scheme uses quantum Zeno dynamics and asymmetric encoding for a one-step gate, with only a pulse on central qudit A and no spacing or resonator-frequency adjustments.In the non-resonant case, the phase can be tuned through pulse Rabi frequency, detuning, and interaction time.Source: §I · p. 2
II. MODEL AND EFFECTIVE DYNAMICS
Two resonators, each hosting a four-level fluxonium qudit, are linked by a common fluxonium coupler, with logical states encoded asymmetrically across the qudits. Under g ≫ Ω, discarding fast-oscillating terms yields effective dynamics for tunable non-resonant and π-phase resonant gates.
II. MODEL AND EFFECTIVE DYNAMICS
- The two resonators each host a four-level fluxonium qudit and connect capacitively through a common fluxonium qudit A; qubits 1 and 2 use |f⟩, |g⟩ as logical states, while A uses |f⟩, |s⟩.The resonator modes couple to |e⟩↔|g⟩ transitions, and a classical microwave pulse drives the |sA⟩↔|eA⟩ transition.Source: §II · pp. 2–3
- For g ≫ Ω, the derivation discards fast-oscillating terms to obtain an effective Hamiltonian.The initial states |f1f2sA⟩ and |f1g2sA⟩ remain unchanged under the effective dynamics; the exchanged state |g1f2sA⟩ evolves similarly by symmetry.Source: §II · pp. 3–4
- In the non-resonant case, |g1g2sA⟩ alone acquires the tunable phase δ = Ω²t/3∆, while the other computational states remain unchanged.At δ = π, adding a Hadamard gate on qubit A gives a three-qubit Toffoli gate.Source: §II · p. 5
- At resonance, a full Rabi cycle returns |g1g2sA⟩ with a π phase shift, producing a three-qubit controlled phase gate.The stated cycle time is t = √3π/Ω.Source: §II · p. 5
- Figure 2 plots real state-coefficient parts over time for three initial states under non-resonant and resonant conditions; the stated parameters are Ω = 0.1g and ∆ = g.Blue, green, and red identify |f1f2sA⟩, |f1g2sA⟩, and |g1g2sA⟩, respectively.Source: Figure 2 · p. 6, §II · p. 6
III. DISCUSSIONS AND NUMERICAL ANALYSIS
Numerical simulations test the three-qubit phase gate in non-resonant and resonant regimes, including sensitivity to coupling errors and decoherence. The results indicate high fidelity under the modeled conditions, with different dominant decoherence sources in the two regimes.
III. DISCUSSIONS AND NUMERICAL ANALYSIS
- The simulated system acquires a π phase while returning to its initial state at τ = 300π/g in the non-resonant case and at τ′ = 3π/g in the resonant case.The non-resonant parameters are Ω = 0.1g and ∆ = g; the resonant case uses Ω = 0.1g and ∆ = 0.Source: §III · p. 6
- With |δg1(2)| = 10%g, fidelity reduction is smaller than 3%, and fidelity remains higher than 97% under the tested parameter deviations.The coupling-error test assumes equal qudit-resonator couplings in the ideal scheme.Source: §III · pp. 6–7
- For κ = γ = 0.1g, fidelity remains larger than 75%; qubit relaxation is greatly suppressed off resonance, while it is the main decoherence source at resonance.The passage attributes this regime difference to detuning off resonance and resonant interaction on resonance.Source: §III · p. 7, Figure 4 · p. 7
- Using cited circuit-QED parameters, the authors estimate fidelity above 99% may be feasible, and report a 24 ns resonant π-phase gate.The cited parameter set is g = 2π × 360 MHz, κ−1 = 1 µs, and γ−1 = 25 µs.Source: §III · p. 7
IV. GENERALIZATION TO N-QUBIT PHASE GATE
The proposal extends the gate to N qubits using N−1 resonator-hosted qudits coupled to a common qudit. In a seven-qubit simulation, the target state acquires the stated phase shift in both non-resonant and resonant regimes.
IV. GENERALIZATION TO N-QUBIT PHASE GATE
- The N-qubit setup uses N−1 resonators, each hosting a qudit, coupled to a common qudit A.Source: §IV · p. 7
- Under g, ∆≫Ω, only |g1g2g3...gN−1sA⟩ receives a phase shift exp(iΩ2t/N∆) in the asymmetric encoding.Qubits 1 through N−1 use |f⟩ and |g⟩ as logical states, while qudit A uses |f⟩ and |s⟩.Source: §IV · p. 8
- For seven qubits, the target state acquires a π phase at gt≈2200 off resonance, while the resonant gate takes 36 ns.The non-resonant phase shift agrees with the stated theoretical value of 700π; the resonant result matches the theoretical value.Source: §IV · pp. 8–9, Figure 6 · p. 8
V. SUMMARY
The paper proposes a one-step circuit-QED multiqubit tunable phase gate using quantum Zeno dynamics and asymmetric logical-state encoding. It reports high-fidelity gate completion, with a tunable gate in the non-resonant case and a faster π-phase gate after a full Rabi cycle in the resonant case.
V. SUMMARY
- The effective dynamics yields high fidelity, with a tunable phase gate off resonance and a π-phase gate after a full Rabi cycle at resonance.Source: §V · p. 9
- The gate requires one-step evolution without individual qudit addressing or adjustments to qudit level spacings and cavity-mode frequency.Source: §V · p. 9
- The scheme is generalized to N-qubit gates, and the paper investigates parameter errors and decoherence from resonator decay and qudit relaxation.Source: §V · p. 9