IBM Heron Processors: Advanced Quantum Devices

• IBM Heron Processors are advanced superconducting quantum devices that enable both circuit- and measurement-based quantum computing with hardware-specific optimizations.
• They enhance output state fidelity by reducing gate count and circuit depth, as demonstrated by improved Mermin inequality test results from ~0.72 to 0.90.
• They support measurement-based protocols such as t-designs and randomized benchmarking, providing insights into noise sensitivity, circuit scaling, and quantum supremacy challenges.

IBM Heron Processors are advanced superconducting quantum computing devices that extend the capabilities demonstrated in earlier IBM quantum platforms. These processors serve as a testbed for both sophisticated circuit-based and measurement-based quantum computing protocols, enabling research into circuit optimization, nonclassicality detection, random unitary ensemble synthesis, and robust randomized benchmarking. The Heron architecture builds upon previous generations such as QX2, QX4, and ibmq_toronto/sydney/hanoi, addressing key challenges of noise reduction and connectivity to support experiments targeting higher fidelity and more demanding quantum protocols.

1. Hardware-Aware Circuit Optimization

Circuit optimization for IBM processors, and by plausible extension the Heron series, centers on reducing both the quantum gate count and circuit depth in Clifford+T circuits. The optimization procedure is twofold: first, every CNOT gate not natively supported by the connectivity graph is decomposed via qubit swapping, implementation on nearest-neighbor pairs, and restoration of logical order. Cost tables specific to the hardware architecture map these transformations and quantify the number of additional gates and circuit levels introduced. Second, all possible mappings of logical to physical qubits are considered—120 permutations for five-qubit processors—with the mapping yielding the minimal total gate and depth costs selected.

Key steps in the algorithm:

1. For each CNOT, look up optimal transformation in the hardware-specific cost table.
2. Substitute CNOTs with corresponding sequences; simplify the circuit by shortening gate sequences (e.g., cancel adjacent Hadamards).
3. Exhaustively search all logical-to-physical qubit assignments for the mapping with minimal cumulative cost.
4. Output an optimized circuit with reduced gate count and circuit levels.

A formal cost function is used:

$$\text{cost}(C) = \alpha (\text{Gate Count}) + \beta (\text{Levels})$$

The optimization problem is to minimize $\text{cost}(C_\text{opt})$ while maintaining logical circuit equivalence.

The Heron processors, owing to their anticipated increased connectivity and possibly reduced error rates, can leverage these circuit optimization strategies by constructing cost tables tailored to their specific couplings and gate characteristics, as well as by more sophisticated logic-to-physical mapping algorithms to further suppress overall circuit complexity (Sisodia et al., 2018).

2. Fidelity Enhancement Through Optimization

Reducing gate counts and circuit depth directly translates to increased output state fidelity, as each additional operation in a quantum circuit accumulates errors stemming from decoherence and gate imperfections. Experimental results in an IBM 5-qubit environment showed a clear increase in fidelity for implementation of the Mermin inequality: an unoptimized circuit achieved a fidelity of approximately 0.72, while the optimized counterpart yielded 0.90. Fidelity is computed via the Uhlmann formula:

$$F = \operatorname{Tr}\left[ \sqrt{ \sqrt{\rho_1} \, \rho_2 \, \sqrt{\rho_1} } \right]$$

where $\rho_1$ is the ideal (theoretical) state and $\rho_2$ is the experimentally realized (noisy) state.

This quantitative improvement validates the utility of cost-aware optimization not only for simple algorithms but also for depth-sensitive quantum protocols and applications targeting the limits of device performance (Sisodia et al., 2018).

3. Measurement-Based Quantum Protocols and t-Designs

IBM Heron Processors support not only gate-based algorithms but also protocols derived from measurement-based quantum computing (MBQC), including the realization of pseudorandom unitary ensembles such as t-designs. A measurement-based t-design typically involves preparing a graph (or linear cluster) state of $n$ qubits, then applying single-qubit measurements in adaptive or pre-selected bases to induce unitaries on the remaining qubits. For instance, an exact single-qubit 3-design is implemented using a 6-qubit linear cluster, with operations of the form:

$U_m(\phi) = H Z^m R_z(\phi)$

where $m$ is the measurement outcome. For the entire measurement sequence on a 6-qubit chain, the unitary is composed as:

$$U_{\mathbf{m}}(\vec{\phi}) = U_{m_5}(\phi_5) \cdots U_{m_1}(\phi_1)$$

In experiments carried out on IBM superconducting processors (e.g., ibmq_toronto, ibmq_sydney), approximate random ensembles could be generated, with channel tomography showing that the realized units passed 1-design tests (average fidelities of 0.82–0.87 after readout error mitigation) but failed for 2- or 3-design criteria. The key limiting factor was identified as depolarizing noise, which increases with both gate complexity and resource state size (Strydom et al., 2022). For Heron-class processors, further reduction of this noise is necessary to achieve high-fidelity t-design generation, which is significant for cryptographic and statistical sampling protocols in quantum information science.

4. Randomized Benchmarking and Noise Sensitivity

Measurement-based interleaved randomized benchmarking has been implemented on IBM processors to evaluate the fidelity of measurement-based gate realizations, including Hadamard and T gates. The procedure alternates (“interleaves”) a target gate with random unitaries selected from a measurement-based 2-design, generating sequences of the form:

$G U_m \, G U_{m-1} \dots G U_1,$

where each $U_i$ is a 2-design unitary. The survival probability over $m$ repetitions for both reference (without $G$) and interleaved (with $G$) sequences is fitted to exponential decay: $$F_{\text{ref}}(m) = A_{\text{ref}}\, p_{\text{ref}}^m + B_{\text{ref}}$$

$$F_{\text{int}}(m) = A_{\text{int}}\, p_{\text{int}}^m + B_{\text{int}}$$

The Haar-averaged gate fidelity is then extracted as:

$$F_G \approx 1 - \frac{d-1}{d} [1 - (p_{\text{int}} / p_{\text{ref}})],\qquad d=2$$

Experiments indicate single-qubit gate fidelities of 0.977 (Hadamard) and 0.972 (T), with good agreement to independent process tomography. Noise sensitivity was probed by increasing cluster state length (thus artificially increasing opportunities for error); fidelities for a 4-qubit cluster Hadamard implementation dropped from 0.894 (4-qubit) to 0.820 (6-qubit), providing empirical calibration for noise accumulation. This approach is fundamental for validating and comparing hardware platforms in scenarios relevant to scaling up quantum processors (Strydom et al., 2022).

5. Detection of Nonclassicality and Quantum Supremacy Prospects

Optimized IBM Heron processors facilitate strong empirical tests of quantum nonclassicality. When implementing protocols such as the Mermin inequality, optimized circuits allowed experimental violation measures to increase from $\langle M_3 \rangle – 2 = 0.85$ (unoptimized) to 1.126 (optimized), with absolute values well above classical bounds and improved alignment with quantum mechanical predictions. Enhanced circuit efficiency thus improves the potential to observe weaker signatures of nonlocality and quantum advantage in actual device runs (Sisodia et al., 2018).

The reduction of circuit costs and corresponding noise accumulation is critical when targeting quantum supremacy—that is, implementing computations for which classical simulation becomes infeasible. The cumulative benefit of circuit-depth reduction, low-noise t-design generation, and rigorous benchmarking protocols collectively underlie the technological roadmap for demonstrating quantum supremacy on devices such as IBM Heron, although persistent challenges remain due to scaling-related decoherence, crosstalk, and calibration errors.

6. Comparative Analysis and Scaling Implications

Empirical results across several IBM platforms show a recurring trade-off between the theoretical capability to realize complex protocol (e.g., higher-order t-designs, larger cluster states) and practical device limitations associated with noise. While larger cluster states in theory support higher-order randomization, in practice, increased qubit number and circuit size exacerbate depolarizing noise, resulting in lower effective design order and fidelity. Tests on 5-qubit clusters (ibmq_sydney) yielded superior channel fidelities and higher pass rates for 2-design criteria than 6-qubit experiments on ibmq_toronto, underlining the importance of both hardware advances and algorithmic minimization of circuit overhead in achieving robust quantum information processing (Strydom et al., 2022).

This comparative insight directly informs the optimization of quantum workloads for Heron-class and future processors, emphasizing the need for hardware-algorithm co-design to approach theoretical device limits, as well as favoring more compact resource state designs under present noise models.

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Table: Summary of Key Performance Metrics in IBM Processors

Protocol	Qubit Resource	Average Channel Fidelity	Limiting Factor
Optimized Mermin Test	3	0.90	Gate/level count
Exact 3-design	6	0.87 (mitigated)	Depolarizing noise
Approximate 2-design	5	Higher than 6-qubit test	Resource size/noise
RB: Hadamard (standard)	2	0.977	Baseline device noise
RB: Hadamard (6-qubit)	6	0.820	Error accumulation

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In summary, IBM Heron Processors serve as a critical platform for experimentation across the cutting edge of quantum circuit optimization, fidelity benchmarking, nonclassicality witnessing, and pseudorandom unitary synthesis. Results to date show that hardware-specific optimization, minimal circuit overhead, and tailored benchmarking protocols are essential for realizing the full theoretical and empirical potential of current and next-generation superconducting quantum devices.