#VirtualZGates

[govindhtech]

Virtual-Z Gates And Symmetric Collation In Quantum Circuits

Virtual-Z-Gates

Pioneering research has discovered a previously overlooked element that greatly affects quantum computer integrity and performance:  quantum gates compilation, especially for Virtual-Z gates. The paper reveals that seemingly minor software-level changes in how instantaneous gates are handled can affect a quantum system's error and decoherence risk. On IBM's ibm_sherbrooke cloud quantum processor and the in-house MUNINN processor.

Quantum processors require a few calibrated native gates. These native gates work with VZ gates to perform vital tasks like the Y gate. Virtual-Z gates are unique because they are instantaneous and error-free. Physical Z-gates require genuine rotations around the Bloch sphere's z-axis, but VZ gates are software phase offsets. Combined with X-type gates, this flexibility simplifies gate decomposition and circuit compilation and allows SU(2) gate design. However, this new study reveals that real-world open quantum systems have a hidden penalty for this flexibility.

Bad Things About Asymmetric Compilation

The paper examines symmetric and asymmetric compilation for VZ-rotated gates.

Imbalanced compilation Asymmetric compilation defines gates like the Y gate by performing the whole VZ phase shift before the pulse on platforms like Qiskit. For example, an X gate and Rz(-π) VZ gate are typically used to build an asymmetric Y gate (Y^asym). Though technically comparable to a true Y gate in a perfect, closed system, this asymmetry method causes major problems in open quantum systems:

When quantum states leave the (x,y) plane of the Bloch sphere, asymmetric compilation forces them to adopt different paths. For instance, the Rz(-π) gate swaps the |-i▩ and |+i▩ states before the X gate in Y^asym. Therefore, when the next physical X gate, |-i⟩ passes through the stable ground state |0⟩ and |+i⟩ passes through the unstable excited state |1⟩. The Asymmetric Fidelity Decay This trajectory difference causes asymmetric fidelity deterioration between initial states. The |-i⟩ state has a lower relaxation rate and better fidelity than |+i⟩ over repeated operations. This breaks the intended behaviour of a correctly calibrated gate, which should act independently of input state.

The Symmetric Compilation Promise

In contrast, the study strongly favours symmetric compilation.

The VZ phase shift is distributed across the physical pulse using this manner. Y^sym = Rz(π/2) X Rz(-π/2) for the Y gate.

Symmetric compilation offers numerous benefits:

When using symmetric compilation, states like |±i⟩ remain within the Bloch sphere's (x,y) plane during gate operation. They do not have different relaxation rates because they do not split into unstable excited states. In symmetric compilation, the fidelities of |±i⟩ states decline uniformly and are almost equivalent. The balanced decrease of a calibrated gate was empirically validated on MUNINN and IBM_Sherbrooke processors.

Important Effect on DD Sequences

Dynamical Decoupling (DD) sequences, which protect qubits from external noise, are especially affected by compilation process choice.

Experimental data suggests that the XY4 DD sequence can be transformed to UR4 (XY4^asym = UR4) via an asymmetric Y gate compilation. Unlike the universal XY4, UR4 does not suppress X-type interactions or multi-axis blunders, which reduces noise suppression.

However, symmetric compilation ensures that the intended gate operations are kept, ensuring a correct execution of the desired DD sequence (such as XY4). Effective use of the X-bar gate (X̄) is crucial for robust DD sequences and other robust DD sequences.

Finding Pulse Interference Errors

In addition to gate composition, pulse interference causes coherence errors, according to the study. Even in DD sequences designed to resist coherent errors, impedance mismatches in microwave control lines can produce fidelity oscillations.

The study found that prolonging the temporal gap between pulses (doubling or tripling the pulse interval τ) can significantly lessen or eliminate pulse interference effects. This confirms past observations that DD performance was not greatest with short pulse intervals. Proper VZ gate decomposition, which ensures resilient sequence implementation, is needed to identify pulse interference from coherent pulse faults such phase and rotation problems.

Quantum Computing Implications

These findings emphasise the importance of carefully compiling VZ gates for quantum algorithms and error-suppression techniques. Asymmetric compilations, like DD sequences, can degrade quantum algorithms and misinterpret experimental results. Symmetric compilation also improved multi-qubit workloads like GHZ-state preservation.

Future work will improve gate compilation techniques, incorporate symmetric approaches into advanced error-correction protocols, and address pulse interference issues to increase quantum gates and quantum computation fidelity.