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I'm currently conducting experiments on unitary t-designs, utilizing random Clifford and T gates within the Qiskit framework. My goal is to simulate quantum circuits that involve the application of a single T-gate across various system sizes. However, as I increase the number of qubits in my system, I encounter memory limitations that prevent the simulation from proceeding.

ValueError: too many subscripts in einsum

This error occurs when I increase my system size to $n=16$ qubits. I want to simulate my system up to $n=40$ qubits to get quality results.

Are there method/library that will help me simulate higher qubit system? Could be any language or library?

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On IBM Quantum platform, a universal simulator is limited by 32 qubits. There is also 64-qubit simulator Clifford+T which could be suitable for your problem.

You can also run your circuit on 127-qubit backends (Brisbane, Osaka and Kyoto). On the other hand, I am not sure if you would be able to extract relevant results for 40 qubits. Because of short decoherence times of current QPUs, the results can be completely blured. I would recommend starting with small number of qubits and then gradually increase their count.

Please bear in mind that if you have a free access to IBM Quantum platform real QPUs, you are limited by 10 minutes of computing time on real QPUs. Increasing number of qubits leads to higher consumption of the computing time. Simulators, like simulator_extended_stabilizer (63 qb) or simulator_mps (100 qb) are for free completely (i.e. they do not consume free computational time).

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  • $\begingroup$ Is there any way to efficiently simulate it in my local system. Cause i believe the premium for IBM quantum is expensive. Qiskit can efficiently simulate Clifford system if we use stabilizer simulator. But I need to include single T gate which makes the system non stabilizer. If there are any library or simulator that does this efficiently on local machine. $\endgroup$ Apr 9 at 16:02
  • $\begingroup$ @AsimSharma: You can use 'simulator_extended_stabilizer' (63 qb) or 'simulator_mps' (100 qb) on IBM Quantum. Those are for free. However, T gate cannot be simulated efficiently in general. It depends on your circuit structure. Increasing number of T gates, number of entangled qubits and strength of the entanglement lead to less and less efficient simulation. $\endgroup$ Apr 9 at 18:34
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    $\begingroup$ Are these simulators local or cloud? $\endgroup$
    – MonteNero
    Apr 9 at 22:33
  • $\begingroup$ @MonteNero: Those are cloud simulator. $\endgroup$ Apr 10 at 4:29
  • $\begingroup$ @AsimSharma: If the answer is ok for you, could you please accept it? $\endgroup$ Apr 11 at 6:09

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