A Design Overview for A Simulation Infrastructure for Exploring Quantum Architecture

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A Design Overview for A Simulation
Infrastructure for Exploring Quantum Architecture

• Dean Copsey?, Mark Oskin?, Andrew Cross?, Tzvetan
  Metodiev?,
• Frederic T. Chong?, Isaac Chuang?, John
  Kubiatowicz?
• ?University of California at Davis, ?University
  of Washington,
• ?Massachusetts Institute of Technology,
  ?University of California at Berkeley

QARC Quantum Architectural Research Center MIT
UCDavis UC Berkeley UWashington
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The Case for Better Tools

• Current Simulation Tools
• Model algorithms, not architecture
• Incorporate complete state information
• We Need
• Hardware and system simulation
• Scalability
• We Want
• Reasonable error bounds without state

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Quantum Computation

• Quantum State Qubits
• Bits are 0i or 1i or a superposition
• a 0ib 1i
• Complex values a and b describe the probability
  of a given state being the one observed
  (measured)
• Two qubits occupy four states, simultaneously
• a 00ib 01i g 10id 11i
• n qubits have 2n states in superposition
• Sx cxxi
• A single operation affects all 2n states!

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Quantum Computation

• Operators
• An operator maps a state onto one or more other
  states, similar to NOT, AND, and OR gates
• inverts a and b Phase inversion
• Hadamard mixer (b ?-b )
• (a ? a b , b ? a -b ) SWAP - exchanges the
• CNOT - two-qubit XOR values of two qubits
• (b ?a ?b )
• Measure the state of a qubit - 0 or 1

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Classical Simulators

• Different Levels for Different Goals
• Physical Level
• Simulate new devices and technologies
• Gate Level / HDL
• Explore devices and designs
• Functional Level
• Instruction sets and special units
• Language Level
• Compilers and optimization

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Quantum Architectural Simulation

• Physical Level
• Gates
• Primitives available from the technology
• Latency
• No state transition information
• Measurement
• Latency
• Communication Primitives
• Passive Decoherence / Gate Decoherence

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Physical Level
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Error Correction

• Qubits are sensitive quantum phenomena
• If it is easy to interact with the qubit, it is
  also sensitive to noise, or decoherence
• Proposed technologies have a probability of
• failure of 10-510-8 per gate
• Measurement destroys state, so simple redundancy
  doesnt work

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Error Correction

• a 0Li b 1Li a 000i b 111i
• X12, X23 measure pairwise-parity

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Error Correction

• Measuring the parity leaves the system consistent
  with the measured value
• Errors are quantized!
• Simple operators correct errors
• Bit-flip and phase errors 7,1,3 can correct
  a single error in any of three dimensions
• Encoded data can be manipulated without decoding!

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Error-Code Tree
49,1,7
7,1,3
Physical qubits 1,1,1

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Quantum Architectural Simulation

• Hardware Design Level - Basic Structures
• Error correction blocks
• Entropy exchange units
• Known-state purification
• Communication Constraints

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Quantum Architectural Simulation

• Hardware Design Level - Composed Structures
• Error-code trees
• ALUs, cache, memory
• Communication channels
• Swap channels
• Ballistic transport channels
• Teleportation channels

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Tree Structure

• Layout includes space for classical control, but
  not the control itself

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Communication

• Communication in the Skinner-Kane Model
• Operators are limited to interaction between
  neighbors
• Data movement requires a swap channel, with
  swaps alternating between pairs

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Ballistic Transport

• Move the physical quantum container
• Possibly more robust than swapping
• Errors include
• Phase shifts
• Heating (vibrational energy)

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Einsteins Paradox EPR Pairs

• An EPR Pair
• If one qubit is measures 0, the other must also
• EPR Pairs Are Necessary for Teleportation

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Quantum Teleportation

• bi and ci are entangled. By entangling, ai
  and bi, and measuring, ci now has the original
  value of ai!

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Language Support

• Algorithms Are Translated to Gates
• Gates Are Constrained and Scheduled
• Error Mitigation Occurs in Structures
• Small structures can be simulated with complete
  state information
• Mitigation mediated by measurement
• Composition of structures still an open problem

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The Grail

• Behavior of Complex Quantum Systems
• Total number of gates
• Running time
• Correctness of design
• Reliability of Operation
• Model error behavior for structures
• Bound error behavior for complex systems