A new method for creating non-Gaussian phase gates has been developed, key components for achieving universal continuous-variable (CV) quantum computation. The approach utilises qubit-oscillator Rabi control to synthesise polynomial phase gates with interaction times that scale favourably, polylogarithmically, with the desired accuracy.

This analytical construction avoids complex numerical optimisation procedures and is readily applicable to larger, more complex quantum systems, demonstrating near optimal efficiency as confirmed by established lower bounds on synthesis time. By successfully simulating CV quantum dynamics and implementing an algorithm solving linear partial differential equations, qubit-oscillator Rabi control is a powerful primitive within CV quantum information processing.

Polylogarithmic Scaling Achieves Faster Continuous-Variable Quantum Gate Synthesis

Total interaction time for synthesising polynomial phase gates has been reduced to O(log(R−1)/2+o(1/ε)), representing an improvement over previous methods requiring O(1/ε) via Fourier-Trotter approaches or O(log(1/ε)) using QSP control. This advance crosses a critical threshold, enabling potentially faster and more efficient routes toward high precision quantum gate operations within continuous-variable (CV) quantum computation; previously, achieving comparable accuracy demanded substantially longer processing times.

Researchers at University of Electronic Science and Technology, in collaboration with Tsinghua University and Yangtze Delta Industrial Innovation Centre of Quantum Science and Technology, demonstrated this polylogarithmic scaling through an analytically constructed Rabi sequence, a series of interactions between qubits and oscillators, avoiding complex numerical optimisation procedures.

The team accomplished this by constructing the Rabi sequence analytically, bypassing computationally intensive numerical optimisation typically used for designing such sequences. Furthermore, they established a lower bound of Ω(log(R−1)/2(1/ε)), confirming that their synthesis is close to being as efficient as theoretically possible given current limitations.

Qubit-oscillator Rabi control enables efficient compilation for continuous-variable quantum computing

Qubit-oscillator Rabi control establishes an efficient, analytically compilable, and near-optimal primitive for continuous-variable (CV) quantum information processing. Continuous-variable quantum computation provides a natural framework for processing quantum information encoded in bosonic modes; the continuous degrees of freedom naturally match the structure of many problems in quantum simulation. This representation supports applications ranging from bosonic simulation and CV quantum search to algorithms solving differential equations, with potential computational advantages under suitable assumptions.

Universal CV quantum computation requires supplementing Gaussian operations with non-Gaussian elements. A canonical choice is the cubic phase gate, but many platforms lack native tunable cubic interactions. Existing approaches based on resource states or nonlinearities can realise these gates yet remain experimentally demanding. Hybrid qubit-oscillator platforms offer an alternative route where an ancillary qubit mediates effective oscillator dynamics, architectures arising in trapped-ion and superconducting systems featuring accessible Rabi interactions coupling a qubit linearly to an oscillator quadrature.

By interleaving these interactions with single-qubit rotations and postselecting the qubit at sequence end, one can induce effective transformations on the oscillator. Numerical protocols have demonstrated high-fidelity approximations to nonlinear phase gates without revealing how interaction time scales as error decreases. An exact finite synthesis would eliminate this precision dependence; however, no finite postselected Rabi sequence restricted to a single oscillator quadrature can exactly realise a polynomial phase gate.

Therefore, the central question is how slowly required interaction time grows with increasing precision. A polylogarithmic dependence on 1/ε, rather than polynomial, provides an exponential improvement in asymptotic cost. Achieving such scaling calls for systematically compiling linear qubit-oscillator interactions into accurate nonlinear transformations. Generalised quantum signal processing (GQSP) offers an analytic framework constructing control sequences whose matrix elements realise bounded Laurent polynomials P(U) of a unitary U, with length governed by the degree needed to approximate the target operation.

This framework has been adapted to bosonic control; QSP suppresses cross-Kerr errors under dispersive coupling with O(log(1/ε)) sequence length. For quadrature coupling, oscillator-qubit GQSP combines QSP with Fourier approximation achieving O(log(1/ε)) sequence length for fixed periodic phase functions. While Fourier-Trotter approaches can generate gates, reducing first-order error requires sequence length O(1/ε). Polynomial phase gates pose a distinct challenge because their phases are nonperiodic and oscillate rapidly with amplitude, meaning both the approximation region and required bandwidth must grow as precision demands increase.

Whether such gates can be synthesised by linear Rabi control with polylogarithmic total interaction time, approaching the fundamental limit, is central to this work. Pulse parameters are obtained analytically through GQSP without variational optimisation; this approximation guarantees a postselection success probability of at least (1 −ε). They further proved the lower bound Ttot = Ω(log(R−1)/2(1/ε)) for same-quadrature sequences showing near optimality.

This construction extends to compositions enabling efficient simulation of a universal CV gate set, preserving polylogarithmic dependence on 1/ε. As applications, they simulated representative dynamics and implemented an algorithm solving a linear elliptic equation establishing qubit-oscillator Rabi control as an efficient primitive for CV quantum information processing. In many algorithms, one is primarily interested in preparing a target output state from readily preparable input.

They required h PN −eiT p( X)i |ψ⟩ ≤ε for every normalized |ψ⟩∈Hn. Each contributes only phase factors e±itjx/2 so resulting function is a finite sum of exponentials satisfying nontrivial linear differential equation. The target eiT p(x), however, does not satisfy such an equation when p is nonlinear. This equality is impossible because functions have incompatible properties; rigorous proof given in Supplemental Material Sec A.

Error from |x| > L is exponentially small so approximating eiT p(x) requires PN(x) on window [−L, L]. Simplifying yields N = O logR/2+o(1/ε); guarantees success probability of at least (1 −ε). Normalized output differs from ideal state by at most 2ε in norm. Once polynomial PN is known GQSP determines Rabi axes without optimisation. Proofs are provided in Supplemental Material Secs B-D. Construction applies to rotated quadratures Q replacing X with it target phase and pulse.

In finite dimensional models elementary gates treated as zero time operations so gate count characterizes complexity; CV parameters can grow unboundedly, squeezing counts single, but interaction grows parameter fixed coupling strength. They showed this is fundamental limit same quadrature setting.

Non-Gaussian gates present a difficulty for universal continuous-variable (CV) quantum computation because their required nonlinearities are difficult to engineer. To address this challenge, an efficient qubit-oscillator Rabi synthesis scheme is developed for polynomial phase gates with total interaction time scaling polylogarithmically with the inverse target error ε. For readily preparable initial states within a finite Fock subspace Hn, a degree-R phase gate can be approximated by an analytically constructed Rabi sequence with total time O(log(R−1)/2+o(1/ε)).

This construction needs no numerical optimisation and extends naturally to arbitrarily large multimode systems. A lower bound of Ω(log(R−1)/2(1/ε)) on the total time is also established demonstrating near optimality of this synthesis.

Rapid gate creation advances continuous-variable quantum computation

Scientists have unlocked faster building blocks for CV computers: non-Gaussian gates enabling complex calculations beyond simpler systems. The team’s method uses precisely timed interactions between qubits and oscillators creating these with reduced time; their current demonstration relies on preparing initial states relatively easy to produce experimentally. Acknowledging reliance simple inputs does not diminish significance findings, as those represent a practical step towards computations.

The research demonstrated an efficient way to create polynomial phase gates, essential components of continuous-variable (CV) quantum computing, using qubit-oscillator Rabi control. This approach allows the construction of degree-R phase gates with total interaction time scaling at O(log(R−1)/2+o(1/ε)), meaning gate creation becomes faster as error decreases. Because this method requires no numerical optimisation and works across multiple systems, it offers a potentially scalable route for CV information processing. Researchers used this scheme to simulate quantum dynamics and solve linear partial differential equations demonstrating its functionality within existing computational frameworks.

👉 More information
🗞 Near-optimal synthesis of non-Gaussian phase gates via qubit-oscillator Rabi control
✍️ Zhen Yang, Shan Jin, Zi-Wen Liu and Xiaoting Wang
🧠 ArXiv: https://arxiv.org/abs/2609.09132

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