Using the extraordinary sensitivity of Andreev interferometers to the superconducting phase difference associated with currents, we measure the persistent current quantum states in superconducting loops interrupted by Josephson junctions. Straightforward electrical resistance measurements of the interferometers give continuous read-out of the states, allowing us to construct the energy spectrum of the quantum circuit. The probe is estimated to be more precise and faster than previous methods, and can measure the local phase difference in a wide range of superconducting circuits.PACS numbers: 03.67. Lx, 85.25.Cp , 85.25.Dq Superconducting circuits consisting of loops interrupted by Josephson junctions show persistent current states that are promising for implementation in a quantum computer [1]. Spectroscopy and coherent quantum dynamics of the circuits have been successfully investigated by determining the switching-to-voltage-stateprobability of an attached superconducting quantum interference device (SQUID) [2]; however, a single switching measurement is low resolution and strongly disturbs both the circuit and the SQUID itself. This revives the fundamental problem of fast high resolution quantum measurements of the persistent current states. The conceptual and technological advance reported here is based on the fact that a persistent current in a quantum circuit is associated with the gradient of the superconducting phase χ of the macroscopic wavefunction describing the circuit. The problem of measuring the current reduces to a measurement of the corresponding phase difference θ q across the Josephson junctions.To measure θ q with a minimum of disruption we use an Andreev interferometer [3,4]. Our Andreev interferometers, shown in the scanning electron microscope images in Figs. 1a and b, are crossed normal (N ) silver conductors a-b and c-d, with contacts to a pair of superconducting (S) aluminium wires at the points c and d. The N/S interfaces play the role of mirrors reflecting electrons via an unusual mechanism first described by Andreev [5]. In Andreev reflection, an electron which is incident on the normal side of the N/S interface evolves into a hole, which retraces the electron trajectory on the N -side, and a Cooper pair is created on the S-side. There is a fundamental relationship between the macroscopic phase of the superconductors and the microscopic phase of the quasiparticles [6]: the hole gains an extra phase equal to the macroscopic phase χ, and correspondingly the electron acquires an extra phase −χ. This leads to phase-periodic oscillations in the resistance R A between the points a and b of the interferometer. It should be emphasized that the macroscopic phase is probed by quasiparticles with energies much less than the superconducting gap, so there is no "quasiparticle poisoning" of the superconductor.We investigate a Josephson quantum circuit with an attached Andreev interferometer, as shown in Figs. 1a and c. To probe the phase difference within the Josephson circuit, superconducting ...