Virtual-Z Gates
A previously underappreciated factor that significantly affects the integrity and performance of quantum computers has been revealed by groundbreaking research: the compilation process of quantum gates, especially those that use Virtual-Z gates. The work shows that seemingly little software-level changes in how these instantaneous gates are handled can have a significant influence on a quantum system’s vulnerability to mistakes and decoherence. It was carried out on both IBM’s ibm_sherbrooke cloud quantum processor and the in-house MUNINN processor.
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A small number of native gates that have already been calibrated are frequently used in quantum processors. These native gates are combined with VZ gates to carry out other essential activities, such as the Y gate. The instantaneous and error-free nature of virtual-Z gates makes them special. In contrast to physical Z-gates, which necessitate real rotations around the Bloch sphere’s z-axis, VZ gates are only implemented as software phase offsets. When paired with X-type gates, this flexibility makes gate decomposition and circuit compilation easier and allows for the design of any SU(2) gate. This new study, however, shows that in open quantum systems found in the real world, this flexibility has a hidden cost.
The Pitfalls of Asymmetric Compilation
The paper looks into both symmetric and asymmetric compilation techniques for gates with VZ rotations.
- Asymmetric compilation Platforms like Qiskit frequently employ asymmetric compilation, which defines gates like the Y gate by applying the whole VZ phase shift prior to the actual pulse. For instance, an X gate and a Rz(-π) VZ gate are commonly used to construct an asymmetric Y gate (Y^asym).
This asymmetry method creates serious issues in open quantum systems even though it is technically equivalent to a real Y gate in a perfect, closed system:
- Divergent Bloch Sphere Trajectories: When quantum states depart the (x,y) plane of the Bloch sphere, asymmetric compilation compels them to take distinct paths. The Rz(-π) gate, for example, immediately switches the |-i▩ and |+i⟩ states before the actual X gate under Y^asym. As a result, during the next physical X gate, |-i⟩ passes through the stable ground state |0⟩ while |+i⟩ passes through the unstable excited state |1⟩.
- Asymmetric Fidelity Decay: Asymmetric fidelity decay between beginning states is caused by this disparity in trajectories. In comparison to |+i⟩, the |-i⟩ state has a lower relaxation rate and retains greater fidelity over repeated operations. The intended behavior of a properly calibrated gate, which should behave consistently independent of the input state, is essentially broken by this.
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The Promise of Symmetric Compilation
The study, on the other hand, significantly supports a symmetric compilation approach.
- The VZ phase shift is dispersed throughout the physical pulse using this method. This indicates that Y^sym = Rz(π/2) X Rz(-π/2) for the Y gate.
Symmetric compilation has many advantages: - Maintained (x,y) Plane Trajectories: States such as |±i⟩ stay inside the Bloch sphere’s (x,y) plane during the gate operation when symmetric compilation is used. Since they do not diverge into unstable excited states, they do not have varying relaxation rates.
- Balanced Fidelity: As a result, under symmetric compilation, the fidelities of |±i⟩ states degrade uniformly and are almost similar. A properly calibrated gate is characterized by this balanced decline, which was empirically confirmed on both MUNINN and IBM_Sherbrooke processors.
Critical Impact on Dynamical Decoupling (DD) Sequences
For Dynamical Decoupling (DD) sequences, which are essential pulse patterns intended to shield qubits from external noise, the compilation method selection has especially dire repercussions.
- Sequence Misidentification: The work provides experimental evidence that the widely used XY4 DD sequence can be successfully converted into the UR4 sequence (XY4^asym = UR4) with the use of an asymmetric Y gate compilation. This is crucial since UR4 significantly reduces noise suppression capabilities by not suppressing X-type interactions or multi-axis mistakes, in contrast to the universal XY4.
- Correct Implementation: On the other hand, symmetric compilation guarantees that the intended gate operations are maintained, guaranteeing a faithful implementation of the desired DD sequence (such as XY4). The proper application of the X-bar gate (X̄), which is also essential for robust DD sequences, and other robust DD sequences are covered by this.
Uncovering Pulse Interference Errors
The study finds that interference between successive pulses is a substantial source of coherent errors in addition to gate composition. Even in DD sequences that are intended to be resistant to other coherent faults, these interference effects which may be caused by impedance mismatches in microwave control lines can create unforeseen oscillations in fidelity.
- Mitigation by Pulse gap Optimization: The study discovered that these pulse interference effects can be considerably reduced or even abolished by purposefully lengthening the time gap between successive pulses (doubling or tripling the pulse interval τ). This clarifies earlier findings that the shortest pulse intervals did not result in the best DD performance. Only with proper VZ gate decomposition, which guarantees the implementation of the planned resilient sequences, can the impacts of pulse interference be distinguished from other coherent pulse faults (such as phase and rotation errors).
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Implications for Quantum Computing
These results highlight how crucial it is to carefully compile VZ gates while creating quantum algorithms and error-suppression strategies. In addition to DD sequences, asymmetric compilations can result in inferior performance in quantum algorithms and inaccurate interpretations of experimental data. Additionally, symmetric compilation produced better performance in multi-qubit tasks like GHZ-state preservation.
To improve the fidelity of quantum gates and quantum computation in general, future work will concentrate on improving gate compilation techniques, incorporating these symmetric approaches into sophisticated error-correction protocols, and further addressing pulse interference issues.
