ECC Framework

The QECC library offers means for automatic implementation and evaluation of error-correcting codes for quantum computing [1]. More precisely, the library allows to automatically apply different error correction schemes to quantum circuits provided as OpenQASM files or Qiskit QuantumCircuit objects. The “protected” quantum circuits can then be exported again in the form of OpenQASM files or can be directly used for noise-aware quantum circuit simulation. For the latter case, a wrapper script which makes use of the provided framework to apply error correction schemes to circuits and directly simulate those circuits using Qiskit is provided.

Usage

Having the Python package installed, error correction can be applied to a quantum circuit using apply_ecc(), like so

from mqt import qecc
from qiskit import QuantumCircuit

file = "path/to/qasm/file.qasm"  # Path to the OpenQASM file the quantum circuit shall be loaded from
ecc = "Q7Steane"  # Error correction code that shall be applied to the quantum circuit
ecc_frequency = 100  # After how many times a qubit is used, error correction is applied

result = qecc.apply_ecc(file, ecc, ecc_frequency)

circ = QuantumCircuit().from_qasm_str(result["circ"])
print(circ)

Currently, the error correction schemes Q3Shor, Q5Laflamme, Q7Steane, Q9Shor, Q9Surface, and Q18Surface are supported.

A wrapper script for applying error correction to quantum circuits (provided as OpenQASM) and performing a noise-aware quantum circuit simulation (using Qiskit) is provided. The script can be used like this:

$ ecc_qiskit_wrapper -ecc Q7Steane -fq 100 -m D -p 0.0001 -n 2000 -fs aer_simulator_stabilizer -s 0 -f  ent_simple1000_n2.qasm
_____Trying to simulate with D(prob=0.0001, shots=2000, n_qubits=17, error correction=Q7Steane) Error______
State |00> probability 0.515
State |01> probability 0.0055
State |10> probability 0.0025
State |11> probability 0.477

The script offers a help function, which displays available parameters:

$ ecc_qiskit_wrapper --help
usage: ecc_qiskit_wrapper [-h] [-m M] [-p P] [-n N] [-s S] -f F [-e E] [-fs FS] [-ecc ECC] [-fq FQ] [-mc MC] [-cf CF]

Qiskit wrapper for the ECC Framework

options:
  -h, --help  show this help message and exit
  -m M        Define the error_channels (e.g., -m APD), available errors channels are amplitude damping (A), phase
              flip (P), bit flip (B), and depolarization (D) (Default="D")
  -p P        Set the noise probability (Default=0.001)
  -n N        Set the number of shots for the simulation (Default=2000)
  -s S        Set a seed (Default=0)
  -f F        Path to a OpenQASM file
  -e E        Export circuit with applied ECC as OpenQASM circuit instead of simulating it (e.g., -e
              "/path/to/new/openqasm_file") (Default=None)
  -fs FS      Specify a simulator (Default="aer_simulator_stabilizer", which is fast but does not support non-Clifford
              gates. Available: [AerSimulator('aer_simulator'), AerSimulator('aer_simulator_statevector'),
              AerSimulator('aer_simulator_density_matrix'), AerSimulator('aer_simulator_stabilizer'),
              AerSimulator('aer_simulator_matrix_product_state'), AerSimulator('aer_simulator_extended_stabilizer'),
              AerSimulator('aer_simulator_unitary'), AerSimulator('aer_simulator_superop'),
              QasmSimulator('qasm_simulator'), StatevectorSimulator('statevector_simulator'),
              UnitarySimulator('unitary_simulator'), PulseSimulator('pulse_simulator')]
  -ecc ECC    Specify an ECC to be applied to the circuit. Currently available are "none", "Q3Shor", "Q5Laflamme",
              "Q7Steane", "Q9Shor", "Q9Surface", and "Q18Surface" (Default=Q7Steane)
  -fq FQ      Specify after how many qubit usages error correction is applied to it (Default=100)

Supported ECCs

Properties

Properties of available error-correcting codes

Feature	Q3Shor [2]	Q5Laflamme [3]	Q7Steane [4]	Q9Shor [2]	Q9Surface [5]	Q18Surface [6]
able to detect bit flips	✔️	✔️	✔️	✔️	✔️	✔️
able to detect phase flips	✖️	✔️	✔️	✔️	✔️	✖️*
#qubits for n logical qubits	3n+2	5n+4	7n+3	9n+8	9n+8	36n
#classical bits (total)	2	5	3	8	8	16

* Planned to work, but not fully implemented yet

Available logical operations

Available operations for each error-correcting code

Operation	Q3Shor [2]	Q5Laflamme [3]	Q7Steane [4]	Q9Shor [2]	Q9Surface [5]	Q18Surface [6]
Pauli (X, Y, Z)	✔️	✔️	✔️	✔️	✔️	✔️
controlled Pauli (CX,CY,CZ)	✔️	✖️	✔️	✔️	✔️	✖️
Hadamard	⚠️	✖️	✔️	✖️	✔️	✔️
S, S†, T, T†	✔️	✖️	✔️	✖️	✖️	✖️

⚠️ = operation is applied without the scheme of the error-correcting code (i.e. decoding and encoding is performed before/afterwards, respectively, and the operation is encoded as-is)