Questions about the provided examples

[KuanYuChang]

Hi there,

It seems that the examples provided in this repo are decomposed into elementary operations and written in OpenQASM format. Is there any instructions for preparing decomposed quantum circuits or even for the other format, e.g., Real?

Sincerely.

[burgholzer]

Hi,

That is correct. Our tool assumes that the circuit to be mapped has already been composed into a sequence of elementary gates (i.e., single- or two-qubit gates) supported by the device it shall be mapped to.
At the moment, we have not integrated any approaches for carrying out this synthesis or decomposition step into the JKQ QMAP tool.
However, you could, for example, use IBM's Qiskit to generate such decomposed circuits and dump them to .qasm files.

As for .real files: Since these typically realize reversible functionality, they rely mainly on multi-controlled Toffoli and Fredkin gates.
Consequently, a straightforward synthesis approach would be to sequentially apply any known decomposition of these gates into elementary gates.

In case of further questions, do not hesitate to ask!

Best regards,
Lukas

[KuanYuChang]

Hi Lukas,

Thanks for your quick reply, I will take my time to look into the transpiling process provided by IBM's Qiskit.

Sincerely,
Kuan-Yu

[burgholzer]

You are welcome!
I'll close this issue for now. In case of further questions do not hesitate to ask.

Best regards,
Lukas

[KuanYuChang]

Hi Lukas,

Another question about decomposing quantum circuits using basis gates, ['x', 'h', 't', 'tdg', 'cx'], is there any tips or suggestions to work around it?

Take alu-v4_36 for example, the circuit could be represented in MCT-Library as following:

OPENQASM 2.0;
include "qelib1.inc";
qreg q[5];
mcx q[4],q[3],q[2],q[1];
cx q[3],q[4];
ccx q[1],q[3],q[2];
x q[2];
ccx q[4],q[2],q[0];
ccx q[0],q[4],q[2];
cx q[2],q[4];

When I tried to decompose alu-v4_36 using Qiskit, it says:

"Cannot unroll the circuit to the given basis, ['x', 'h', 't', 'tdg', 'cx']. No rule to expand instruction u1."

However, the same circuit provided in examples of this repo decomposed only based on ['x', 'h', 't', 'tdg', 'cx'].

Sincerely,
Kuan-Yu

---

The following provides additional information:

• alu-v4_36 in this repo: https://github.com/iic-jku/qmap/blob/master/examples/alu-v4_36.qasm
• alu-v4_36 from RevLib: http://www.revlib.org/doc/real/alu-v4_36.real
• Version of Qiskit: 0.19.0
• Script to reproduce:

import qiskit as qk
circ = qk.QuantumCircuit(5)
circ.mcx([4, 3, 2], 1)
circ.cx(3, 4)
circ.ccx(1, 3, 2)
circ.x(2)
circ.ccx(4, 2, 0)
circ.ccx(0, 4, 2)
circ.cx(2, 4)
circ = qk.transpile(circ, basis_gates=['x', 'h', 't', 'tdg', 'cx'])

• Detail traceback:

Traceback (most recent call last):
  File "produce.py", line 14, in <module>
    circ = qk.transpile(circ, basis_gates=['x', 'h', 't', 'tdg', 'cx'])
  File "${LIB}/python3.6/site-packages/qiskit/compiler/transpile.py", line 210, in transpile
    circuits = parallel_map(_transpile_circuit, list(zip(circuits, transpile_args)))
  File "${LIB}/python3.6/site-packages/qiskit/tools/parallel.py", line 105, in parallel_map
    return [task(values[0], *task_args, **task_kwargs)]
  File "${LIB}/python3.6/site-packages/qiskit/compiler/transpile.py", line 307, in _transpile_circuit
    output_name=transpile_config['output_name'])
  File "${LIB}/python3.6/site-packages/qiskit/transpiler/passmanager.py", line 214, in run
    return self._run_single_circuit(circuits, output_name, callback)
  File "${LIB}/python3.6/site-packages/qiskit/transpiler/passmanager.py", line 277, in _run_single_circuit
    result = running_passmanager.run(circuit, output_name=output_name, callback=callback)
  File "${LIB}/python3.6/site-packages/qiskit/transpiler/runningpassmanager.py", line 115, in run
    dag = self._do_pass(pass_, dag, passset.options)
  File "${LIB}/python3.6/site-packages/qiskit/transpiler/runningpassmanager.py", line 145, in _do_pass
    dag = self._run_this_pass(pass_, dag)
  File "${LIB}/python3.6/site-packages/qiskit/transpiler/runningpassmanager.py", line 157, in _run_this_pass
    new_dag = pass_.run(dag)
  File "${LIB}/python3.6/site-packages/qiskit/transpiler/passes/basis/unroller.py", line 107, in run
    unrolled_dag = self.run(decomposition)  # recursively unroll ops
  File "${LIB}/python3.6/site-packages/qiskit/transpiler/passes/basis/unroller.py", line 107, in run
    unrolled_dag = self.run(decomposition)  # recursively unroll ops
  File "${LIB}/python3.6/site-packages/qiskit/transpiler/passes/basis/unroller.py", line 107, in run
    unrolled_dag = self.run(decomposition)  # recursively unroll ops
  File "${LIB}/python3.6/site-packages/qiskit/transpiler/passes/basis/unroller.py", line 93, in run
    (str(self.basis), node.op.name))
qiskit.exceptions.QiskitError: "Cannot unroll the circuit to the given basis, ['x', 'h', 't', 'tdg', 'cx']. No rule to expand instruction u1."

[burgholzer]

Hi Kuan-Yu,

Qiskit (or in general IBM devices) support the universal gate set ['CX', 'U'] where U(theta, phi,lambda) represents arbitrary single-qubit gates. All of the gates that Qiskit understands are derived from this gate-set. You can find these definitions at https://github.com/Qiskit/qiskit-terra/blob/master/qiskit/qasm/libs/qelib1.inc
There you can see that t = u1(pi/4), tdg = u1(-pi/4) and h = u2(0, pi).

To fix your error just pass basis_gates=['u3', 'cx'] (or anything more specific, like basis_gates=['x', 'h', 't', 'tdg', 'u1', 'u2', 'u3', 'cx']) to the transpile function.

Best regards,
Lukas

[KuanYuChang]

Hi Lukas,

Following your suggestion, I have done the decomposition of alu-v4_36 by passing an additional gate u1, i.e., passing basis_gates=['cx', 'x', 'h', 't', 'tdg', 'u1'], but I'm still wondering how to done it without using u1, i.e., used only ['cx', 'x', 'h', 't', 'tdg'].

Since I only found the reference that decomposing the MCT gate based on NCV-Library, could you provide some reference to decompose the MCT gate based on ['cx', 'x', 'h', 't', 'tdg']?

Sincerely,
Kuan-Yu

[burgholzer]

Hi Kuan-Yu,

In fact u1(pi/4) is equivalent to t. That is just how Qiskit breaks down the operations. There is not really a reason for not including this gate.
Our tool for example will read in the .qasm file and automatically convert u1(pi/4) to t.

The standard reference for this kind of topic would probably be https://arxiv.org/abs/quant-ph/9503016.
Qiskit implements many of the techniques described in https://arxiv.org/abs/1508.03273.
You can look at the source code directly at https://qiskit.org/documentation/_modules/qiskit/circuit/quantumcircuit.html#QuantumCircuit.mcx.

Hope this helps,
Lukas

[KuanYuChang]

Hi Lukas,

I truly appreciate your support, but it seems that the provided reference will take me a long time to understand. I think I will use basis_gates=['cx', 'u3'] for the further circuits for now.

Many thanks,
Kuan-Yu