Verification of Universal Quantum Computation

Functionality

Quantum Computers perform task which are intractable for classical computers. The basic question here would be, "How should one verify the result of a quantum computer? This task is known as quantum verification or verification of quantum computation
Tags: Quantum Functionality, Universal Task

Protocols

• Verification for universal protocols

1. Single-prover prepare-and-send: Verifier can only prepare and send quantum states
   1. Quantum-authentication based verification
   2. Trap-based based verification: uses blind delegated quantum computation
   3. Verification based on repeated runs
2. Single-prover receive-and-measure: Verifier can only receive and measure quantum states
   1. Measurement only verification: uses blind delegated quantum computation
   2. Post-hoc verification: Non-interactive (requires only single round of back and forth communication)
3. Multi-prover entanglement-based: Verifier is completely classical and the provers are entangled
   1. Verification based on CHSH rigidity
   2. Verification based on self-testing graphs
   3. Post-hoc verification
4. Classical Verification of Quantum Computation

• Verification for sub-universal protocols
• Verification of NP-complete problems

Properties

• Problem (Verifiability of BQP computations) statement if formally defined in the following question Does every problem in BQP admit an interactive-proof system in which the prover is restricted to BQP computations?

• Complexity Classes

1. BQP is the class of problems which can be efficiently solved by quantum computers
2. BPP is the class of problems which can be efficiently solved by classical computers.
3. MA (Merlin-Arthur) is the class of problems whose solutions can be verified when given a proof setting called witness.
4. IP (interactive-proof system) is a generalization of MA, which involves back and forth communication between a verifier (a BPP machine) and prover (has unbounded computational power).
5. Protocols 1.1, 1.2 are QPIP protocols and 2.1 is an MIP protocol. QPIP and MIP are classes of decision problems and can be decided by protocols 1.1, 1.2 and 2.1, respectively.

Further Information

• Review Papers

1. Gheorghiu et al (2018)

contributed by Shraddha Singh