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Quantum process tomography (QPT) methods aim at identifying a given quantumprocess. The present paper focuses on the estimation of a unitary process. Thisclass is of particular interest because quantum mechanics postulates that theevolution of any closed quantum system is described by a unitarytransformation. The standard approach of QTP is to measure copies of aparticular set of predetermined (generally pure) states after they have beenmodified by the process to be identified. The main problem with this setup isthat preparing an input state and setting it precisely to a predetermined valueis challenging and thus yields errors. These errors can be decomposed into asum of centred errors (i.e. whose average on all the copies is zero) andsystematic errors that are the same on all the copies, the latter is often themain source of error in QPT. The algorithm we introduce in the current paperworks for any input states that make QPT theoretically possible. The fact thatwe do not require the input states to be precisely set to predetermined valuesmeans that we can use a trick to remove the issue of systematic errors byconsidering that some states are unknown but measured before they go throughthe process to be identified. We achieve this by splitting the copies of eachinput state into several groups and measuring the copies of the $k$-th groupafter they have successively been transferred through $k$ instances of theprocess to be identified (each copy of each input state is only measured once).Using this trick we can compute estimates of the measured states before andafter they go through the process without using the knowledge we might have onthe initial states. We test our algorithm both on simulated data andexperimentally to identify a CNOT gate on a trapped-ions qubit quantumcomputer.

Unitary quantum process tomography with unreliable pure input states